OEIS Similars: A039599, A050155
| ↕ Type | ↕ Trait | ↕ Anum | ↕ Sequence |
|---|---|---|---|
| Std | TriangleT(n, k), 0 ≤ k ≤ n | A085478 | 1 1 1 1 3 1 1 6 5 1 1 10 15 7 1 1 15 35 28 9 1 1 21 70 84 45 11 1 1 28 126 210 165 66 13 1 1 36 210 |
| Std | RevT(n, n - k), 0 ≤ k ≤ n | A054142 | 1 1 1 1 3 1 1 5 6 1 1 7 15 10 1 1 9 28 35 15 1 1 11 45 84 70 21 1 1 13 66 165 210 126 28 1 1 15 91 |
| Std | InvT-1(n, k), 0 ≤ k ≤ n | A039599 | 1 -1 1 2 -3 1 -5 9 -5 1 14 -28 20 -7 1 -42 90 -75 35 -9 1 132 -297 275 -154 54 -11 1 -429 1001 |
| Std | RevInvT-1(n, n - k), 0 ≤ k ≤ n | A050165 | 1 1 -1 1 -3 2 1 -5 9 -5 1 -7 20 -28 14 1 -9 35 -75 90 -42 1 -11 54 -154 275 -297 132 1 -13 77 -273 |
| Std | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A098435 | 1 -1 1 2 -3 1 -8 13 -6 1 56 -92 45 -10 1 -608 1000 -493 115 -15 1 9440 -15528 7662 -1799 245 -21 1 |
| Std | Accsee docs | missing | 1 1 2 1 4 5 1 7 12 13 1 11 26 33 34 1 16 51 79 88 89 1 22 92 176 221 232 233 1 29 155 365 530 596 |
| Std | AccRevsee docs | A038730 | 1 1 2 1 4 5 1 6 12 13 1 8 23 33 34 1 10 38 73 88 89 1 12 57 141 211 232 233 1 14 80 245 455 581 609 |
| Std | AntiDiagsee docs | A034839 | 1 1 1 1 1 3 1 6 1 1 10 5 1 15 15 1 1 21 35 7 1 28 70 28 1 1 36 126 84 9 1 45 210 210 45 1 1 55 330 |
| Std | Diffx1T(n, k) (k+1) | missing | 1 1 2 1 6 3 1 12 15 4 1 20 45 28 5 1 30 105 112 45 6 1 42 210 336 225 66 7 1 56 378 840 825 396 91 |
| Std | RowSum∑ k=0..n T(n, k) | A001519 | 1 2 5 13 34 89 233 610 1597 4181 10946 28657 75025 196418 514229 1346269 3524578 9227465 24157817 |
| Std | EvenSum∑ k=0..n T(n, k) even(k) | A109961 | 1 1 2 6 17 45 117 305 798 2090 5473 14329 37513 98209 257114 673134 1762289 4613733 12078909 |
| Std | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 1 3 7 17 44 116 305 799 2091 5473 14328 37512 98209 257115 673135 1762289 4613732 12078908 |
| Std | AbsSum∑ k=0..n | T(n, k) | | A001519 | 1 2 5 13 34 89 233 610 1597 4181 10946 28657 75025 196418 514229 1346269 3524578 9227465 24157817 |
| Std | DiagSum∑ k=0..n // 2 T(n - k, k) | A000079 | 1 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576 |
| Std | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A027989 | 1 3 10 33 105 324 977 2895 8462 24465 70101 199368 563425 1583643 4430290 12342849 34262337 |
| Std | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A038731 | 1 3 10 32 99 299 887 2595 7508 21526 61251 173173 486925 1362627 3797374 10543724 29180067 80521055 |
| Std | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 3 30 210 1260 13860 180180 180180 6126120 116396280 116396280 2677114440 13385572200 |
| Std | RowGcdGcd k=0..n | T(n, k) | > 1 | A000012 | 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Std | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 3 6 15 35 84 210 495 1287 3003 8008 19448 50388 125970 319770 817190 2042975 5311735 13123110 |
| Std | ColMiddleT(n, n // 2) | missing | 1 1 3 6 15 35 84 210 495 1287 3003 8008 18564 50388 116280 319770 735471 2042975 4686825 13123110 |
| Std | CentralET(2 n, n) | A005809 | 1 3 15 84 495 3003 18564 116280 735471 4686825 30045015 193536720 1251677700 8122425444 52860229080 |
| Std | CentralOT(2 n + 1, n) | A117671 | 1 6 35 210 1287 8008 50388 319770 2042975 13123110 84672315 548354040 3562467300 23206929840 |
| Std | ColLeftT(n, 0) | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Std | ColRightT(n, n) | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Std | BinConv∑ k=0..n C(n, k) T(n, k) | A082759 | 1 2 8 35 160 752 3599 17446 85376 420884 2087008 10398016 52010479 261021854 1313707256 6628095035 |
| Std | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 0 -4 3 24 -40 -145 420 784 -3948 -3024 34320 -3729 -277992 261404 2085083 -3912480 -14151072 |
| Std | TransNat0∑ k=0..n T(n, k) k | A001870 | 0 1 5 19 65 210 654 1985 5911 17345 50305 144516 411900 1166209 3283145 9197455 25655489 71293590 |
| Std | TransNat1∑ k=0..n T(n, k) (k + 1) | A038731 | 1 3 10 32 99 299 887 2595 7508 21526 61251 173173 486925 1362627 3797374 10543724 29180067 80521055 |
| Std | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 7 35 149 576 2088 7229 24179 78727 250873 785448 2423160 7382857 22254247 66460403 196868141 |
| Std | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A007583 | 1 3 11 43 171 683 2731 10923 43691 174763 699051 2796203 11184811 44739243 178956971 715827883 |
| Std | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A087168 | 1 -1 -1 7 -17 23 -1 -89 271 -457 287 967 -4049 8279 -8641 -7193 56143 -139657 194399 -24569 -703889 |
| Std | DiagRow1T(n + 1, n) | A005408 | 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 |
| Std | DiagRow2T(n + 2, n) | A000384 | 1 6 15 28 45 66 91 120 153 190 231 276 325 378 435 496 561 630 703 780 861 946 1035 1128 1225 1326 |
| Std | DiagRow3T(n + 3, n) | A000447 | 1 10 35 84 165 286 455 680 969 1330 1771 2300 2925 3654 4495 5456 6545 7770 9139 10660 12341 14190 |
| Std | DiagCol1T(n + 1, 1) | A000217 | 1 3 6 10 15 21 28 36 45 55 66 78 91 105 120 136 153 171 190 210 231 253 276 300 325 351 378 406 435 |
| Std | DiagCol2T(n + 2, 2) | A000332 | 1 5 15 35 70 126 210 330 495 715 1001 1365 1820 2380 3060 3876 4845 5985 7315 8855 10626 12650 |
| Std | DiagCol3T(n + 3, 3) | A000579 | 1 7 28 84 210 462 924 1716 3003 5005 8008 12376 18564 27132 38760 54264 74613 100947 134596 177100 |
| Std | Polysee docs | missing | 1 1 1 1 2 1 1 5 3 1 1 13 11 4 1 1 34 41 19 5 1 1 89 153 91 29 6 1 1 233 571 436 169 41 7 1 1 610 |
| Std | PolyRow1∑ k=0..1 T(1, k) n^k | A000027 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 |
| Std | PolyRow2∑ k=0..2 T(2, k) n^k | A028387 | 1 5 11 19 29 41 55 71 89 109 131 155 181 209 239 271 305 341 379 419 461 505 551 599 649 701 755 |
| Std | PolyRow3∑ k=0..3 T(3, k) n^k | A123972 | 1 13 41 91 169 281 433 631 881 1189 1561 2003 2521 3121 3809 4591 5473 6461 7561 8779 10121 11593 |
| Std | PolyCol2∑ k=0..n T(n, k) 2^k | A001835 | 1 3 11 41 153 571 2131 7953 29681 110771 413403 1542841 5757961 21489003 80198051 299303201 |
| Std | PolyCol3∑ k=0..n T(n, k) 3^k | A004253 | 1 4 19 91 436 2089 10009 47956 229771 1100899 5274724 25272721 121088881 580171684 2779769539 |
| Std | PolyDiag∑ k=0..n T(n, k) n^k | A094955 | 1 2 11 91 985 13201 211303 3936808 83739041 2003229469 53252096051 1557702562417 49731172316281 |
| Alt | TriangleT(n, k), 0 ≤ k ≤ n | A085478 | 1 1 -1 1 -3 1 1 -6 5 -1 1 -10 15 -7 1 1 -15 35 -28 9 -1 1 -21 70 -84 45 -11 1 1 -28 126 -210 165 |
| Alt | RevT(n, n - k), 0 ≤ k ≤ n | A054142 | 1 -1 1 1 -3 1 -1 5 -6 1 1 -7 15 -10 1 -1 9 -28 35 -15 1 1 -11 45 -84 70 -21 1 -1 13 -66 165 -210 |
| Alt | InvT-1(n, k), 0 ≤ k ≤ n | missing | 1 -1 1 -4 3 1 13 -9 -5 1 140 -98 -50 7 1 -772 540 275 -35 -9 1 -13442 9405 4785 -616 -144 11 1 |
| Alt | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 -1 1 3 -4 1 -5 -9 13 1 7 -50 -98 140 1 -9 -35 275 540 -772 1 11 -144 -616 4785 9405 -13442 1 |
| Alt | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A098435 | 1 1 1 2 3 1 8 13 6 1 56 92 45 10 1 608 1000 493 115 15 1 9440 15528 7662 1799 245 21 1 198272 |
| Alt | Accsee docs | missing | 1 1 0 1 -2 -1 1 -5 0 -1 1 -9 6 -1 0 1 -14 21 -7 2 1 1 -20 50 -34 11 0 1 1 -27 99 -111 54 -12 1 0 1 |
| Alt | AccRevsee docs | missing | 1 -1 0 1 -2 -1 -1 4 -2 -1 1 -6 9 -1 0 -1 8 -20 15 0 1 1 -10 35 -49 21 0 1 -1 12 -54 111 -99 27 -1 0 |
| Alt | AntiDiagsee docs | A034839 | 1 1 1 -1 1 -3 1 -6 1 1 -10 5 1 -15 15 -1 1 -21 35 -7 1 -28 70 -28 1 1 -36 126 -84 9 1 -45 210 -210 |
| Alt | Diffx1T(n, k) (k+1) | missing | 1 1 -2 1 -6 3 1 -12 15 -4 1 -20 45 -28 5 1 -30 105 -112 45 -6 1 -42 210 -336 225 -66 7 1 -56 378 |
| Alt | EvenSum∑ k=0..n T(n, k) even(k) | A109961 | 1 1 2 6 17 45 117 305 798 2090 5473 14329 37513 98209 257114 673134 1762289 4613733 12078909 |
| Alt | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 -1 -3 -7 -17 -44 -116 -305 -799 -2091 -5473 -14328 -37512 -98209 -257115 -673135 -1762289 |
| Alt | AltSum∑ k=0..n T(n, k) (-1)^k | A001519 | 1 2 5 13 34 89 233 610 1597 4181 10946 28657 75025 196418 514229 1346269 3524578 9227465 24157817 |
| Alt | AbsSum∑ k=0..n | T(n, k) | | A001519 | 1 2 5 13 34 89 233 610 1597 4181 10946 28657 75025 196418 514229 1346269 3524578 9227465 24157817 |
| Alt | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 -1 -2 0 3 3 -1 -5 -4 2 7 5 -3 -9 -6 4 11 7 -5 -13 -8 6 15 9 -7 -17 -10 8 19 11 -9 -21 -12 10 23 |
| Alt | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 3 30 210 1260 13860 180180 180180 6126120 116396280 116396280 2677114440 13385572200 |
| Alt | RowGcdGcd k=0..n | T(n, k) | > 1 | A000012 | 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Alt | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 3 6 15 35 84 210 495 1287 3003 8008 19448 50388 125970 319770 817190 2042975 5311735 13123110 |
| Alt | ColMiddleT(n, n // 2) | missing | 1 1 -3 -6 15 35 -84 -210 495 1287 -3003 -8008 18564 50388 -116280 -319770 735471 2042975 -4686825 |
| Alt | CentralET(2 n, n) | A005809 | 1 -3 15 -84 495 -3003 18564 -116280 735471 -4686825 30045015 -193536720 1251677700 -8122425444 |
| Alt | CentralOT(2 n + 1, n) | A117671 | 1 -6 35 -210 1287 -8008 50388 -319770 2042975 -13123110 84672315 -548354040 3562467300 -23206929840 |
| Alt | ColLeftT(n, 0) | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Alt | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 0 -4 -3 24 40 -145 -420 784 3948 -3024 -34320 -3729 277992 261404 -2085083 -3912480 14151072 |
| Alt | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A082759 | 1 -2 8 -35 160 -752 3599 -17446 85376 -420884 2087008 -10398016 52010479 -261021854 1313707256 |
| Alt | TransNat0∑ k=0..n T(n, k) k | A151842 | 0 -1 -1 1 3 2 -2 -5 -3 3 7 4 -4 -9 -5 5 11 6 -6 -13 -7 7 15 8 -8 -17 -9 9 19 10 -10 -21 -11 11 23 |
| Alt | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 -1 -2 0 3 3 -1 -5 -4 2 7 5 -3 -9 -6 4 11 7 -5 -13 -8 6 15 9 -7 -17 -10 8 19 11 -9 -21 -12 10 23 |
| Alt | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A087168 | 1 1 -1 -7 -17 -23 -1 89 271 457 287 -967 -4049 -8279 -8641 7193 56143 139657 194399 24569 -703889 |
| Alt | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A007583 | 1 -3 11 -43 171 -683 2731 -10923 43691 -174763 699051 -2796203 11184811 -44739243 178956971 |
| Alt | DiagRow1T(n + 1, n) | A005408 | 1 -3 5 -7 9 -11 13 -15 17 -19 21 -23 25 -27 29 -31 33 -35 37 -39 41 -43 45 -47 49 -51 53 -55 57 -59 |
| Alt | DiagRow2T(n + 2, n) | A000384 | 1 -6 15 -28 45 -66 91 -120 153 -190 231 -276 325 -378 435 -496 561 -630 703 -780 861 -946 1035 |
| Alt | DiagRow3T(n + 3, n) | A000447 | 1 -10 35 -84 165 -286 455 -680 969 -1330 1771 -2300 2925 -3654 4495 -5456 6545 -7770 9139 -10660 |
| Alt | DiagCol1T(n + 1, 1) | A000217 | -1 -3 -6 -10 -15 -21 -28 -36 -45 -55 -66 -78 -91 -105 -120 -136 -153 -171 -190 -210 -231 -253 -276 |
| Alt | DiagCol2T(n + 2, 2) | A000332 | 1 5 15 35 70 126 210 330 495 715 1001 1365 1820 2380 3060 3876 4845 5985 7315 8855 10626 12650 |
| Alt | DiagCol3T(n + 3, 3) | A000579 | -1 -7 -28 -84 -210 -462 -924 -1716 -3003 -5005 -8008 -12376 -18564 -27132 -38760 -54264 -74613 |
| Alt | Polysee docs | missing | 1 1 1 1 0 1 1 -1 -1 1 1 -1 -1 -2 1 1 0 1 1 -3 1 1 1 1 1 5 -4 1 1 1 -1 -2 -7 11 -5 1 1 0 -1 1 9 -29 |
| Alt | PolyRow1∑ k=0..1 T(1, k) n^k | A000027 | 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 -13 -14 -15 -16 -17 -18 -19 -20 -21 -22 -23 -24 -25 -26 |
| Alt | PolyRow2∑ k=0..2 T(2, k) n^k | A028387 | 1 -1 -1 1 5 11 19 29 41 55 71 89 109 131 155 181 209 239 271 305 341 379 419 461 505 551 599 649 |
| Alt | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 1 -1 1 1 -7 -29 -71 -139 -239 -377 -559 -791 -1079 -1429 -1847 -2339 -2911 -3569 -4319 -5167 -6119 |
| Alt | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 0 -1 1 9 -199 3691 -73254 1607521 -39088169 1048062951 -30789776159 984771132841 -34088956044012 |
| Rev | TriangleT(n, k), 0 ≤ k ≤ n | A054142 | 1 1 1 1 3 1 1 5 6 1 1 7 15 10 1 1 9 28 35 15 1 1 11 45 84 70 21 1 1 13 66 165 210 126 28 1 1 15 91 |
| Rev | InvT-1(n, k), 0 ≤ k ≤ n | A098435 | 1 -1 1 2 -3 1 -8 13 -6 1 56 -92 45 -10 1 -608 1000 -493 115 -15 1 9440 -15528 7662 -1799 245 -21 1 |
| Rev | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 -1 1 -3 2 1 -6 13 -8 1 -10 45 -92 56 1 -15 115 -493 1000 -608 1 -21 245 -1799 7662 -15528 9440 |
| Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A039599 | 1 -1 1 2 -3 1 -5 9 -5 1 14 -28 20 -7 1 -42 90 -75 35 -9 1 132 -297 275 -154 54 -11 1 -429 1001 |
| Rev | Accsee docs | A038730 | 1 1 2 1 4 5 1 6 12 13 1 8 23 33 34 1 10 38 73 88 89 1 12 57 141 211 232 233 1 14 80 245 455 581 609 |
| Rev | AccRevsee docs | missing | 1 1 2 1 4 5 1 7 12 13 1 11 26 33 34 1 16 51 79 88 89 1 22 92 176 221 232 233 1 29 155 365 530 596 |
| Rev | AntiDiagsee docs | missing | 1 1 1 1 1 3 1 5 1 1 7 6 1 9 15 1 1 11 28 10 1 13 45 35 1 1 15 66 84 15 1 17 91 165 70 1 1 19 120 |
| Rev | Diffx1T(n, k) (k+1) | missing | 1 1 2 1 6 3 1 10 18 4 1 14 45 40 5 1 18 84 140 75 6 1 22 135 336 350 126 7 1 26 198 660 1050 756 |
| Rev | RowSum∑ k=0..n T(n, k) | A001519 | 1 2 5 13 34 89 233 610 1597 4181 10946 28657 75025 196418 514229 1346269 3524578 9227465 24157817 |
| Rev | EvenSum∑ k=0..n T(n, k) even(k) | A108479 | 1 1 2 7 17 44 117 305 798 2091 5473 14328 37513 98209 257114 673135 1762289 4613732 12078909 |
| Rev | OddSum∑ k=0..n T(n, k) odd(k) | A099511 | 0 1 3 6 17 45 116 305 799 2090 5473 14329 37512 98209 257115 673134 1762289 4613733 12078908 |
| Rev | AbsSum∑ k=0..n | T(n, k) | | A001519 | 1 2 5 13 34 89 233 610 1597 4181 10946 28657 75025 196418 514229 1346269 3524578 9227465 24157817 |
| Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | A052535 | 1 1 2 4 7 14 26 50 95 181 345 657 1252 2385 4544 8657 16493 31422 59864 114051 217286 413966 788674 |
| Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A038731 | 1 3 10 32 99 299 887 2595 7508 21526 61251 173173 486925 1362627 3797374 10543724 29180067 80521055 |
| Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A027989 | 1 3 10 33 105 324 977 2895 8462 24465 70101 199368 563425 1583643 4430290 12342849 34262337 |
| Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 3 30 210 1260 13860 180180 180180 6126120 116396280 116396280 2677114440 13385572200 |
| Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | A000012 | 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Rev | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 3 6 15 35 84 210 495 1287 3003 8008 19448 50388 125970 319770 817190 2042975 5311735 13123110 |
| Rev | ColMiddleT(n, n // 2) | missing | 1 1 3 5 15 28 84 165 495 1001 3003 6188 18564 38760 116280 245157 735471 1562275 4686825 10015005 |
| Rev | CentralET(2 n, n) | A005809 | 1 3 15 84 495 3003 18564 116280 735471 4686825 30045015 193536720 1251677700 8122425444 52860229080 |
| Rev | CentralOT(2 n + 1, n) | A025174 | 1 5 28 165 1001 6188 38760 245157 1562275 10015005 64512240 417225900 2707475148 17620076360 |
| Rev | ColLeftT(n, 0) | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Rev | ColRightT(n, n) | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Rev | BinConv∑ k=0..n C(n, k) T(n, k) | A082759 | 1 2 8 35 160 752 3599 17446 85376 420884 2087008 10398016 52010479 261021854 1313707256 6628095035 |
| Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 0 -4 -3 24 40 -145 -420 784 3948 -3024 -34320 -3729 277992 261404 -2085083 -3912480 14151072 |
| Rev | TransNat0∑ k=0..n T(n, k) k | A054444 | 0 1 5 20 71 235 744 2285 6865 20284 59155 170711 488400 1387225 3916061 10996580 30737759 85573315 |
| Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | A027989 | 1 3 10 33 105 324 977 2895 8462 24465 70101 199368 563425 1583643 4430290 12342849 34262337 |
| Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 7 38 173 701 2628 9329 31811 105178 339373 1073593 3341160 10256065 31115071 93447278 278184461 |
| Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A001835 | 1 3 11 41 153 571 2131 7953 29681 110771 413403 1542841 5757961 21489003 80198051 299303201 |
| Rev | DiagRow1T(n + 1, n) | A000217 | 1 3 6 10 15 21 28 36 45 55 66 78 91 105 120 136 153 171 190 210 231 253 276 300 325 351 378 406 435 |
| Rev | DiagRow2T(n + 2, n) | A000332 | 1 5 15 35 70 126 210 330 495 715 1001 1365 1820 2380 3060 3876 4845 5985 7315 8855 10626 12650 |
| Rev | DiagRow3T(n + 3, n) | A000579 | 1 7 28 84 210 462 924 1716 3003 5005 8008 12376 18564 27132 38760 54264 74613 100947 134596 177100 |
| Rev | DiagCol1T(n + 1, 1) | A005408 | 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 |
| Rev | DiagCol2T(n + 2, 2) | A000384 | 1 6 15 28 45 66 91 120 153 190 231 276 325 378 435 496 561 630 703 780 861 946 1035 1128 1225 1326 |
| Rev | DiagCol3T(n + 3, 3) | A000447 | 1 10 35 84 165 286 455 680 969 1330 1771 2300 2925 3654 4495 5456 6545 7770 9139 10660 12341 14190 |
| Rev | Polysee docs | missing | 1 1 1 1 2 1 1 5 3 1 1 13 11 4 1 1 34 43 19 5 1 1 89 171 97 29 6 1 1 233 683 508 181 41 7 1 1 610 |
| Rev | PolyRow1∑ k=0..1 T(1, k) n^k | A000027 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 |
| Rev | PolyRow2∑ k=0..2 T(2, k) n^k | A028387 | 1 5 11 19 29 41 55 71 89 109 131 155 181 209 239 271 305 341 379 419 461 505 551 599 649 701 755 |
| Rev | PolyRow3∑ k=0..3 T(3, k) n^k | A106734 | 1 13 43 97 181 301 463 673 937 1261 1651 2113 2653 3277 3991 4801 5713 6733 7867 9121 10501 12013 |
| Rev | PolyCol2∑ k=0..n T(n, k) 2^k | A007583 | 1 3 11 43 171 683 2731 10923 43691 174763 699051 2796203 11184811 44739243 178956971 715827883 |
| Rev | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 4 19 97 508 2683 14209 75316 399331 2117473 11228332 59541067 315732481 1674257764 8878212019 |
| Rev | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 2 11 97 1165 17621 320503 6799528 164643641 4476859381 134982195491 4467463316867 160963885064581 |
| Rev:Inv | TriangleT(n, k), 0 ≤ k ≤ n | A098435 | 1 -1 1 2 -3 1 -8 13 -6 1 56 -92 45 -10 1 -608 1000 -493 115 -15 1 9440 -15528 7662 -1799 245 -21 1 |
| Rev:Inv | RevT(n, n - k), 0 ≤ k ≤ n | missing | 1 1 -1 1 -3 2 1 -6 13 -8 1 -10 45 -92 56 1 -15 115 -493 1000 -608 1 -21 245 -1799 7662 -15528 9440 |
| Rev:Inv | InvT-1(n, k), 0 ≤ k ≤ n | A054142 | 1 1 1 1 3 1 1 5 6 1 1 7 15 10 1 1 9 28 35 15 1 1 11 45 84 70 21 1 1 13 66 165 210 126 28 1 1 15 91 |
| Rev:Inv | RevInvT-1(n, n - k), 0 ≤ k ≤ n | A085478 | 1 1 1 1 3 1 1 6 5 1 1 10 15 7 1 1 15 35 28 9 1 1 21 70 84 45 11 1 1 28 126 210 165 66 13 1 1 36 210 |
| Rev:Inv | Accsee docs | missing | 1 -1 0 2 -1 0 -8 5 -1 0 56 -36 9 -1 0 -608 392 -101 14 -1 0 9440 -6088 1574 -225 20 -1 0 -198272 |
| Rev:Inv | AccRevsee docs | missing | 1 1 0 1 -2 0 1 -5 8 0 1 -9 36 -56 0 1 -14 101 -392 608 0 1 -20 225 -1574 6088 -9440 0 1 -27 435 |
| Rev:Inv | AntiDiagsee docs | missing | 1 -1 2 1 -8 -3 56 13 1 -608 -92 -6 9440 1000 45 1 -198272 -15528 -493 -10 5410688 326144 7662 115 1 |
| Rev:Inv | Diffx1T(n, k) (k+1) | missing | 1 -1 2 2 -6 3 -8 26 -18 4 56 -184 135 -40 5 -608 2000 -1479 460 -75 6 9440 -31056 22986 -7196 1225 |
| Rev:Inv | RowSum∑ k=0..n T(n, k) | A000007 | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| Rev:Inv | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 -1 3 -14 102 -1116 17348 -364424 9945032 -341955856 14461211568 -737593705184 44646910492512 |
| Rev:Inv | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 1 -3 14 -102 1116 -17348 364424 -9945032 341955856 -14461211568 737593705184 -44646910492512 |
| Rev:Inv | AltSum∑ k=0..n T(n, k) (-1)^k | missing | 1 -2 6 -28 204 -2232 34696 -728848 19890064 -683911712 28922423136 -1475187410368 89293820985024 |
| Rev:Inv | AbsSum∑ k=0..n | T(n, k) | | missing | 1 2 6 28 204 2232 34696 728848 19890064 683911712 28922423136 1475187410368 89293820985024 |
| Rev:Inv | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 -1 3 -11 70 -706 10486 -214303 5744610 -195106886 8178199743 -414387808297 24957037859416 |
| Rev:Inv | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 -1 1 -4 28 -304 4720 -99136 2705344 -93021952 3933869824 -200646919168 12145256872960 |
| Rev:Inv | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 1 -1 4 -28 304 -4720 99136 -2705344 93021952 -3933869824 200646919168 -12145256872960 |
| Rev:Inv | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 6 312 57960 2585292000 294657588553440 4297597259162887680 104662129953941584435006485120 |
| Rev:Inv | RowGcdGcd k=0..n | T(n, k) | > 1 | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Rev:Inv | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 3 13 92 1000 15528 326144 8900224 306029952 12941912960 660101905408 39956293561344 |
| Rev:Inv | ColMiddleT(n, n // 2) | missing | 1 -1 -3 13 45 -493 -1799 37817 141465 -4864601 -18458187 941466949 3605408261 -255502317701 |
| Rev:Inv | CentralET(2 n, n) | missing | 1 -3 45 -1799 141465 -18458187 3605408261 -984817607951 358414037848881 -167629051362787475 |
| Rev:Inv | CentralOT(2 n + 1, n) | missing | -1 13 -493 37817 -4864601 941466949 -255502317701 92542589508337 -43122229926167473 |
| Rev:Inv | ColLeftT(n, 0) | A005439 | 1 -1 2 -8 56 -608 9440 -198272 5410688 -186043904 7867739648 -401293838336 24290513745920 |
| Rev:Inv | ColRightT(n, n) | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Rev:Inv | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 0 -3 14 -81 538 -1228 -143286 8604511 -447697708 24539711385 -1480261186244 99280806257444 |
| Rev:Inv | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 2 9 66 735 11764 257320 7375898 268023135 12028325418 652882585773 42134951479848 |
| Rev:Inv | TransNat0∑ k=0..n T(n, k) k | missing | 0 1 -1 4 -28 304 -4720 99136 -2705344 93021952 -3933869824 200646919168 -12145256872960 |
| Rev:Inv | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 1 -1 4 -28 304 -4720 99136 -2705344 93021952 -3933869824 200646919168 -12145256872960 |
| Rev:Inv | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 1 -2 14 -152 2360 -49568 1352672 -46510976 1966934912 -100323459584 6072628436480 |
| Rev:Inv | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 -1 3 -23 321 -6969 216403 -9090383 496138849 -34118990929 2885763323715 -294376553464487 |
| Rev:Inv | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 3 15 129 1833 39891 1239063 52050657 2840852913 195362789187 16523665489599 1685578188850977 |
| Rev:Inv | DiagRow1T(n + 1, n) | A000217 | -1 -3 -6 -10 -15 -21 -28 -36 -45 -55 -66 -78 -91 -105 -120 -136 -153 -171 -190 -210 -231 -253 -276 |
| Rev:Inv | DiagRow2T(n + 2, n) | A212501 | 2 13 45 115 245 462 798 1290 1980 2915 4147 5733 7735 10220 13260 16932 21318 26505 32585 39655 |
| Rev:Inv | DiagRow3T(n + 3, n) | missing | -8 -92 -493 -1799 -5180 -12684 -27594 -54846 -101508 -177320 -295295 -472381 -730184 -1095752 |
| Rev:Inv | DiagCol1T(n + 1, 1) | missing | 1 -3 13 -92 1000 -15528 326144 -8900224 306029952 -12941912960 660101905408 -39956293561344 |
| Rev:Inv | DiagCol2T(n + 2, 2) | missing | 1 -6 45 -493 7662 -160944 4392080 -151019712 6386577984 -325747233152 19717640536704 |
| Rev:Inv | DiagCol3T(n + 3, 3) | missing | 1 -10 115 -1799 37817 -1032088 35488176 -1500785520 76547530752 -4633459799936 328356359247488 |
| Rev:Inv | Polysee docs | missing | 1 -1 1 2 0 1 -8 0 1 1 56 0 0 2 1 -608 0 2 2 3 1 9440 0 -12 4 6 4 1 -198272 0 132 -4 12 12 5 1 |
| Rev:Inv | PolyRow1∑ k=0..1 T(1, k) n^k | A000027 | -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 |
| Rev:Inv | PolyRow2∑ k=0..2 T(2, k) n^k | A002378 | 2 0 0 2 6 12 20 30 42 56 72 90 110 132 156 182 210 240 272 306 342 380 420 462 506 552 600 650 702 |
| Rev:Inv | PolyRow3∑ k=0..3 T(3, k) n^k | A242659 | -8 0 2 4 12 32 70 132 224 352 522 740 1012 1344 1742 2212 2760 3392 4114 4932 5852 6880 8022 9284 |
| Rev:Inv | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 1 0 2 -12 132 -2048 43016 -1173872 40363024 -1706939904 87062421536 -5269931269824 |
| Rev:Inv | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 2 2 4 -4 88 -1288 27184 -741616 25500448 -1078405600 55004047936 -3329422120000 235943975274880 |
| Rev:Inv | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 0 0 4 24 192 4400 26736 1154944 16795648 -10311552 41654358080 -1961787418624 151337674260480 |
| Inv | TriangleT(n, k), 0 ≤ k ≤ n | A039599 | 1 -1 1 2 -3 1 -5 9 -5 1 14 -28 20 -7 1 -42 90 -75 35 -9 1 132 -297 275 -154 54 -11 1 -429 1001 |
| Inv | RevT(n, n - k), 0 ≤ k ≤ n | A050165 | 1 1 -1 1 -3 2 1 -5 9 -5 1 -7 20 -28 14 1 -9 35 -75 90 -42 1 -11 54 -154 275 -297 132 1 -13 77 -273 |
| Inv | RevInvT-1(n, n - k), 0 ≤ k ≤ n | A054142 | 1 1 1 1 3 1 1 5 6 1 1 7 15 10 1 1 9 28 35 15 1 1 11 45 84 70 21 1 1 13 66 165 210 126 28 1 1 15 91 |
| Inv | Accsee docs | A128899 | 1 -1 0 2 -1 0 -5 4 -1 0 14 -14 6 -1 0 -42 48 -27 8 -1 0 132 -165 110 -44 10 -1 0 -429 572 -429 208 |
| Inv | AccRevsee docs | missing | 1 1 0 1 -2 0 1 -4 5 0 1 -6 14 -14 0 1 -8 27 -48 42 0 1 -10 44 -110 165 -132 0 1 -12 65 -208 429 |
| Inv | AntiDiagsee docs | missing | 1 -1 2 1 -5 -3 14 9 1 -42 -28 -5 132 90 20 1 -429 -297 -75 -7 1430 1001 275 35 1 -4862 -3432 -1001 |
| Inv | Diffx1T(n, k) (k+1) | missing | 1 -1 2 2 -6 3 -5 18 -15 4 14 -56 60 -28 5 -42 180 -225 140 -45 6 132 -594 825 -616 270 -66 7 -429 |
| Inv | RowSum∑ k=0..n T(n, k) | A000007 | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| Inv | EvenSum∑ k=0..n T(n, k) even(k) | A001700 | 1 -1 3 -10 35 -126 462 -1716 6435 -24310 92378 -352716 1352078 -5200300 20058300 -77558760 |
| Inv | OddSum∑ k=0..n T(n, k) odd(k) | A001700 | 0 1 -3 10 -35 126 -462 1716 -6435 24310 -92378 352716 -1352078 5200300 -20058300 77558760 |
| Inv | AltSum∑ k=0..n T(n, k) (-1)^k | A000984 | 1 -2 6 -20 70 -252 924 -3432 12870 -48620 184756 -705432 2704156 -10400600 40116600 -155117520 |
| Inv | AbsSum∑ k=0..n | T(n, k) | | A000984 | 1 2 6 20 70 252 924 3432 12870 48620 184756 705432 2704156 10400600 40116600 155117520 601080390 |
| Inv | DiagSum∑ k=0..n // 2 T(n - k, k) | A000958 | 1 -1 3 -8 24 -75 243 -808 2742 -9458 33062 -116868 417022 -1500159 5434563 -19808976 72596742 |
| Inv | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A000108 | 1 -1 1 -2 5 -14 42 -132 429 -1430 4862 -16796 58786 -208012 742900 -2674440 9694845 -35357670 |
| Inv | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A000108 | 1 1 -1 2 -5 14 -42 132 -429 1430 -4862 16796 -58786 208012 -742900 2674440 -9694845 35357670 |
| Inv | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 6 45 140 3150 207900 21021 2522520 192972780 83140200 4801346550 53006865912 106340934700 |
| Inv | RowGcdGcd k=0..n | T(n, k) | > 1 | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Inv | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 3 9 28 90 297 1001 3640 13260 48450 177650 653752 2414425 8947575 33266625 124062000 463991880 |
| Inv | ColMiddleT(n, n // 2) | missing | 1 -1 -3 9 20 -75 -154 637 1260 -5508 -10659 48279 92092 -427570 -807300 3817125 7152444 -34295052 |
| Inv | CentralET(2 n, n) | A126596 | 1 -3 20 -154 1260 -10659 92092 -807300 7152444 -63882940 574221648 -5188082354 47073334100 |
| Inv | CentralOT(2 n + 1, n) | missing | -1 9 -75 637 -5508 48279 -427570 3817125 -34295052 309722116 -2809118403 25569834459 -233460867500 |
| Inv | ColLeftT(n, 0) | A000108 | 1 -1 2 -5 14 -42 132 -429 1430 -4862 16796 -58786 208012 -742900 2674440 -9694845 35357670 |
| Inv | ColRightT(n, n) | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Inv | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 0 -3 8 -5 -36 140 -176 -441 2600 -4851 -3840 47476 -119952 23400 821408 -2760545 2524176 12872519 |
| Inv | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A174687 | 1 2 9 48 275 1638 9996 62016 389367 2466750 15737865 100975680 650872404 4211628008 27341497800 |
| Inv | TransNat0∑ k=0..n T(n, k) k | A000108 | 0 1 -1 2 -5 14 -42 132 -429 1430 -4862 16796 -58786 208012 -742900 2674440 -9694845 35357670 |
| Inv | TransNat1∑ k=0..n T(n, k) (k + 1) | A000108 | 1 1 -1 2 -5 14 -42 132 -429 1430 -4862 16796 -58786 208012 -742900 2674440 -9694845 35357670 |
| Inv | TransSqrs∑ k=0..n T(n, k) k^2 | A000108 | 0 1 1 -2 5 -14 42 -132 429 -1430 4862 -16796 58786 -208012 742900 -2674440 9694845 -35357670 |
| Inv | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A064062 | 1 -1 3 -13 67 -381 2307 -14589 95235 -636925 4341763 -30056445 210731011 -1493303293 10678370307 |
| Inv | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A089022 | 1 3 15 87 543 3543 23823 163719 1143999 8099511 57959535 418441191 3043608351 22280372247 |
| Inv | DiagRow1T(n + 1, n) | A005408 | -1 -3 -5 -7 -9 -11 -13 -15 -17 -19 -21 -23 -25 -27 -29 -31 -33 -35 -37 -39 -41 -43 -45 -47 -49 -51 |
| Inv | DiagRow2T(n + 2, n) | A014107 | 2 9 20 35 54 77 104 135 170 209 252 299 350 405 464 527 594 665 740 819 902 989 1080 1175 1274 1377 |
| Inv | DiagRow3T(n + 3, n) | missing | -5 -28 -75 -154 -273 -440 -663 -950 -1309 -1748 -2275 -2898 -3625 -4464 -5423 -6510 -7733 -9100 |
| Inv | DiagCol1T(n + 1, 1) | A000245 | 1 -3 9 -28 90 -297 1001 -3432 11934 -41990 149226 -534888 1931540 -7020405 25662825 -94287120 |
| Inv | DiagCol2T(n + 2, 2) | A000344 | 1 -5 20 -75 275 -1001 3640 -13260 48450 -177650 653752 -2414425 8947575 -33266625 124062000 |
| Inv | DiagCol3T(n + 3, 3) | A000588 | 1 -7 35 -154 637 -2548 9996 -38760 149226 -572033 2187185 -8351070 31865925 -121580760 463991880 |
| Inv | Polysee docs | missing | 1 -1 1 2 0 1 -5 0 1 1 14 0 0 2 1 -42 0 1 2 3 1 132 0 -2 4 6 4 1 -429 0 6 2 15 12 5 1 1430 0 -18 12 |
| Inv | PolyRow1∑ k=0..1 T(1, k) n^k | A000027 | -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 |
| Inv | PolyRow2∑ k=0..2 T(2, k) n^k | A002378 | 2 0 0 2 6 12 20 30 42 56 72 90 110 132 156 182 210 240 272 306 342 380 420 462 506 552 600 650 702 |
| Inv | PolyRow3∑ k=0..3 T(3, k) n^k | A053698 | -5 0 1 4 15 40 85 156 259 400 585 820 1111 1464 1885 2380 2955 3616 4369 5220 6175 7240 8421 9724 |
| Inv | PolyCol2∑ k=0..n T(n, k) 2^k | A000957 | 1 1 0 1 -2 6 -18 57 -186 622 -2120 7338 -25724 91144 -325878 1174281 -4260282 15548694 -57048048 |
| Inv | PolyCol3∑ k=0..n T(n, k) 3^k | A126984 | 1 2 2 4 2 12 -12 72 -190 700 -2308 8120 -28364 100856 -360792 1301904 -4727358 17268636 -63405012 |
| Inv | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 0 0 4 30 408 6090 108792 2228310 51665200 1337341896 38235702360 1196772475756 40703663670096 |
| Inv:Rev | TriangleT(n, k), 0 ≤ k ≤ n | A050165 | 1 1 -1 1 -3 2 1 -5 9 -5 1 -7 20 -28 14 1 -9 35 -75 90 -42 1 -11 54 -154 275 -297 132 1 -13 77 -273 |
| Inv:Rev | RevT(n, n - k), 0 ≤ k ≤ n | A039599 | 1 -1 1 2 -3 1 -5 9 -5 1 14 -28 20 -7 1 -42 90 -75 35 -9 1 132 -297 275 -154 54 -11 1 -429 1001 |
| Inv:Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A085478 | 1 1 1 1 3 1 1 6 5 1 1 10 15 7 1 1 15 35 28 9 1 1 21 70 84 45 11 1 1 28 126 210 165 66 13 1 1 36 210 |
| Inv:Rev | Accsee docs | missing | 1 1 0 1 -2 0 1 -4 5 0 1 -6 14 -14 0 1 -8 27 -48 42 0 1 -10 44 -110 165 -132 0 1 -12 65 -208 429 |
| Inv:Rev | AccRevsee docs | A128899 | 1 -1 0 2 -1 0 -5 4 -1 0 14 -14 6 -1 0 -42 48 -27 8 -1 0 132 -165 110 -44 10 -1 0 -429 572 -429 208 |
| Inv:Rev | AntiDiagsee docs | missing | 1 1 1 -1 1 -3 1 -5 2 1 -7 9 1 -9 20 -5 1 -11 35 -28 1 -13 54 -75 14 1 -15 77 -154 90 1 -17 104 -273 |
| Inv:Rev | Diffx1T(n, k) (k+1) | missing | 1 1 -2 1 -6 6 1 -10 27 -20 1 -14 60 -112 70 1 -18 105 -300 450 -252 1 -22 162 -616 1375 -1782 924 1 |
| Inv:Rev | RowSum∑ k=0..n T(n, k) | A000007 | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| Inv:Rev | EvenSum∑ k=0..n T(n, k) even(k) | A001700 | 1 1 3 10 35 126 462 1716 6435 24310 92378 352716 1352078 5200300 20058300 77558760 300540195 |
| Inv:Rev | OddSum∑ k=0..n T(n, k) odd(k) | A001700 | 0 -1 -3 -10 -35 -126 -462 -1716 -6435 -24310 -92378 -352716 -1352078 -5200300 -20058300 -77558760 |
| Inv:Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A000984 | 1 2 6 20 70 252 924 3432 12870 48620 184756 705432 2704156 10400600 40116600 155117520 601080390 |
| Inv:Rev | AbsSum∑ k=0..n | T(n, k) | | A000984 | 1 2 6 20 70 252 924 3432 12870 48620 184756 705432 2704156 10400600 40116600 155117520 601080390 |
| Inv:Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 0 -2 -2 3 7 -3 -19 -1 48 17 -122 -66 327 205 -944 -598 2925 1747 -9563 -5270 32399 16580 |
| Inv:Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A000108 | 1 1 -1 2 -5 14 -42 132 -429 1430 -4862 16796 -58786 208012 -742900 2674440 -9694845 35357670 |
| Inv:Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A000108 | 1 -1 1 -2 5 -14 42 -132 429 -1430 4862 -16796 58786 -208012 742900 -2674440 9694845 -35357670 |
| Inv:Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 6 45 140 3150 207900 21021 2522520 192972780 83140200 4801346550 53006865912 106340934700 |
| Inv:Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Inv:Rev | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 3 9 28 90 297 1001 3640 13260 48450 177650 653752 2414425 8947575 33266625 124062000 463991880 |
| Inv:Rev | ColMiddleT(n, n // 2) | missing | 1 1 -3 -5 20 35 -154 -273 1260 2244 -10659 -19019 92092 164450 -807300 -1442025 7152444 12776588 |
| Inv:Rev | CentralET(2 n, n) | A126596 | 1 -3 20 -154 1260 -10659 92092 -807300 7152444 -63882940 574221648 -5188082354 47073334100 |
| Inv:Rev | CentralOT(2 n + 1, n) | missing | 1 -5 35 -273 2244 -19019 164450 -1442025 12776588 -114108148 1025551163 -9264432775 84045912300 |
| Inv:Rev | ColLeftT(n, 0) | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Inv:Rev | ColRightT(n, n) | A000108 | 1 -1 2 -5 14 -42 132 -429 1430 -4862 16796 -58786 208012 -742900 2674440 -9694845 35357670 |
| Inv:Rev | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 0 -3 8 -5 -36 140 -176 -441 2600 -4851 -3840 47476 -119952 23400 821408 -2760545 2524176 12872519 |
| Inv:Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A174687 | 1 -2 9 -48 275 -1638 9996 -62016 389367 -2466750 15737865 -100975680 650872404 -4211628008 |
| Inv:Rev | TransNat0∑ k=0..n T(n, k) k | A000108 | 0 -1 1 -2 5 -14 42 -132 429 -1430 4862 -16796 58786 -208012 742900 -2674440 9694845 -35357670 |
| Inv:Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | A000108 | 1 -1 1 -2 5 -14 42 -132 429 -1430 4862 -16796 58786 -208012 742900 -2674440 9694845 -35357670 |
| Inv:Rev | TransSqrs∑ k=0..n T(n, k) k^2 | A078718 | 0 -1 5 -14 45 -154 546 -1980 7293 -27170 102102 -386308 1469650 -5616324 21544100 -82907640 |
| Inv:Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A000957 | 1 1 0 1 -2 6 -18 57 -186 622 -2120 7338 -25724 91144 -325878 1174281 -4260282 15548694 -57048048 |
| Inv:Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A007854 | 1 -3 12 -51 222 -978 4338 -19323 86310 -386250 1730832 -7763550 34847796 -156503064 703149438 |
| Inv:Rev | DiagRow1T(n + 1, n) | A000245 | 1 -3 9 -28 90 -297 1001 -3432 11934 -41990 149226 -534888 1931540 -7020405 25662825 -94287120 |
| Inv:Rev | DiagRow2T(n + 2, n) | A000344 | 1 -5 20 -75 275 -1001 3640 -13260 48450 -177650 653752 -2414425 8947575 -33266625 124062000 |
| Inv:Rev | DiagRow3T(n + 3, n) | A000588 | 1 -7 35 -154 637 -2548 9996 -38760 149226 -572033 2187185 -8351070 31865925 -121580760 463991880 |
| Inv:Rev | DiagCol1T(n + 1, 1) | A005408 | -1 -3 -5 -7 -9 -11 -13 -15 -17 -19 -21 -23 -25 -27 -29 -31 -33 -35 -37 -39 -41 -43 -45 -47 -49 -51 |
| Inv:Rev | DiagCol2T(n + 2, 2) | A014107 | 2 9 20 35 54 77 104 135 170 209 252 299 350 405 464 527 594 665 740 819 902 989 1080 1175 1274 1377 |
| Inv:Rev | DiagCol3T(n + 3, 3) | missing | -5 -28 -75 -154 -273 -440 -663 -950 -1309 -1748 -2275 -2898 -3625 -4464 -5423 -6510 -7733 -9100 |
| Inv:Rev | Polysee docs | missing | 1 1 1 1 0 1 1 0 -1 1 1 0 3 -2 1 1 0 -13 10 -3 1 1 0 67 -68 21 -4 1 1 0 -381 538 -195 36 -5 1 1 0 |
| Inv:Rev | PolyRow1∑ k=0..1 T(1, k) n^k | A000027 | 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 -13 -14 -15 -16 -17 -18 -19 -20 -21 -22 -23 -24 -25 -26 |
| Inv:Rev | PolyRow2∑ k=0..2 T(2, k) n^k | A014105 | 1 0 3 10 21 36 55 78 105 136 171 210 253 300 351 406 465 528 595 666 741 820 903 990 1081 1176 1275 |
| Inv:Rev | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 1 0 -13 -68 -195 -424 -785 -1308 -2023 -2960 -4149 -5620 -7403 -9528 -12025 -14924 -18255 -22048 |
| Inv:Rev | PolyCol2∑ k=0..n T(n, k) 2^k | A064062 | 1 -1 3 -13 67 -381 2307 -14589 95235 -636925 4341763 -30056445 210731011 -1493303293 10678370307 |
| Inv:Rev | PolyCol3∑ k=0..n T(n, k) 3^k | A110520 | 1 -2 10 -68 538 -4652 42628 -406856 4001914 -40285724 413049580 -4298523704 45288486436 |
| Inv:Rev | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 0 3 -68 2085 -83544 4174135 -250917624 17669646729 -1428339725360 130449626216811 |
| << | Table | Source | Similars | Index | >> |
Note: The A-numbers are based on a finite number of numerical comparisons. They ignore the sign and the OEIS-offset. Sometimes they differ in the first few values. In such cases, we consider our version to be the better one because it has a common formula as a root. Since the offset of all triangles is 0 also the offset of all sequences is 0.