OEIS Similars: A008290, A098825
| ↕ Type | ↕ Trait | ↕ Anum | ↕ Sequence |
|---|---|---|---|
| Std | TriangleT(n, k), 0 ≤ k ≤ n | A008290 | 1 0 1 1 0 1 2 3 0 1 9 8 6 0 1 44 45 20 10 0 1 265 264 135 40 15 0 1 1854 1855 924 315 70 21 0 1 |
| Std | RevT(n, n - k), 0 ≤ k ≤ n | A098825 | 1 1 0 1 0 1 1 0 3 2 1 0 6 8 9 1 0 10 20 45 44 1 0 15 40 135 264 265 1 0 21 70 315 924 1855 1854 1 0 |
| Std | InvT-1(n, k), 0 ≤ k ≤ n | A055137 | 1 0 1 -1 0 1 -2 -3 0 1 -3 -8 -6 0 1 -4 -15 -20 -10 0 1 -5 -24 -45 -40 -15 0 1 -6 -35 -84 -105 -70 |
| Std | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 0 1 0 -1 1 0 -3 -2 1 0 -6 -8 -3 1 0 -10 -20 -15 -4 1 0 -15 -40 -45 -24 -5 1 0 -21 -70 -105 -84 |
| Std | Accsee docs | missing | 1 0 1 1 1 2 2 5 5 6 9 17 23 23 24 44 89 109 119 119 120 265 529 664 704 719 719 720 1854 3709 4633 |
| Std | AccRevsee docs | missing | 1 1 1 1 1 2 1 1 4 6 1 1 7 15 24 1 1 11 31 76 120 1 1 16 56 191 455 720 1 1 22 92 407 1331 3186 5040 |
| Std | AntiDiagsee docs | missing | 1 0 1 1 2 0 9 3 1 44 8 0 265 45 6 1 1854 264 20 0 14833 1855 135 10 1 133496 14832 924 40 0 1334961 |
| Std | Diffx1T(n, k) (k+1) | missing | 1 0 2 1 0 3 2 6 0 4 9 16 18 0 5 44 90 60 40 0 6 265 528 405 160 75 0 7 1854 3710 2772 1260 350 126 |
| Std | RowSum∑ k=0..n T(n, k) | A000142 | 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 |
| Std | EvenSum∑ k=0..n T(n, k) even(k) | A062282 | 1 0 2 2 16 64 416 2848 22912 205952 2060032 22659328 271913984 3534877696 49488295936 742324422656 |
| Std | OddSum∑ k=0..n T(n, k) odd(k) | A063083 | 0 1 0 4 8 56 304 2192 17408 156928 1568768 17257472 207087616 2692143104 37689995264 565349945344 |
| Std | AltSum∑ k=0..n T(n, k) (-1)^k | A000023 | 1 -1 2 -2 8 8 112 656 5504 49024 491264 5401856 64826368 842734592 11798300672 176974477312 |
| Std | AbsSum∑ k=0..n | T(n, k) | | A000142 | 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 |
| Std | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 0 2 2 13 52 317 2138 16834 149292 1476209 16088808 191589809 2474578188 34452505666 514313005438 |
| Std | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A001563 | 1 1 4 18 96 600 4320 35280 322560 3265920 36288000 439084800 5748019200 80951270400 1220496076800 |
| Std | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A052849 | 1 2 4 12 48 240 1440 10080 80640 725760 7257600 79833600 958003200 12454041600 174356582400 |
| Std | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 1 6 72 1980 629640 75661740 1282617816480 4377895262100360 721520918146760331600 |
| Std | 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 |
| Std | RowMaxMax k=0..n | T(n, k) | | A174318 | 1 1 1 3 9 45 265 1855 14833 133497 1334961 14684571 176214841 2290792933 32071101049 481066515735 |
| Std | ColMiddleT(n, n // 2) | missing | 1 0 0 3 6 20 40 315 630 5544 11088 122430 244860 3181464 6362928 95450355 190900710 3245287760 |
| Std | CentralET(2 n, n) | A281262 | 1 0 6 40 630 11088 244860 6362928 190900710 6490575520 246642054516 10358965584240 476512419579196 |
| Std | CentralOT(2 n + 1, n) | missing | 0 3 20 315 5544 122430 3181464 95450355 3245287760 123321027258 5179482792120 238256209789598 |
| Std | ColLeftT(n, 0) | A000166 | 1 0 1 2 9 44 265 1854 14833 133496 1334961 14684570 176214841 2290792932 32071101049 481066515734 |
| 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) | missing | 1 1 2 12 78 570 4900 48160 530390 6464430 86327388 1252761048 19620649356 329739285876 |
| Std | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 1 2 8 14 82 132 744 4566 -33442 587036 -6952064 87792652 -1082005052 13392493064 -162520998480 |
| Std | TransNat0∑ k=0..n T(n, k) k | A000142 | 0 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 |
| Std | TransNat1∑ k=0..n T(n, k) (k + 1) | A052849 | 1 2 4 12 48 240 1440 10080 80640 725760 7257600 79833600 958003200 12454041600 174356582400 |
| Std | TransSqrs∑ k=0..n T(n, k) k^2 | A052849 | 0 1 4 12 48 240 1440 10080 80640 725760 7257600 79833600 958003200 12454041600 174356582400 |
| Std | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A000354 | 1 1 5 29 233 2329 27949 391285 6260561 112690097 2253801941 49583642701 1190007424825 |
| Std | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A343582 | 1 1 5 -3 105 -807 10413 -143595 2304081 -41453775 829134549 -18240782931 437779321785 |
| Std | DiagRow2T(n + 2, 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 |
| Std | DiagRow3T(n + 3, n) | A007290 | 2 8 20 40 70 112 168 240 330 440 572 728 910 1120 1360 1632 1938 2280 2660 3080 3542 4048 4600 5200 |
| Std | DiagCol1T(n + 1, 1) | A000240 | 1 0 3 8 45 264 1855 14832 133497 1334960 14684571 176214840 2290792933 32071101048 481066515735 |
| Std | DiagCol2T(n + 2, 2) | A000387 | 1 0 6 20 135 924 7420 66744 667485 7342280 88107426 1145396460 16035550531 240533257860 |
| Std | DiagCol3T(n + 3, 3) | A000449 | 1 0 10 40 315 2464 22260 222480 2447445 29369120 381798846 5345183480 80177752655 1282844041920 |
| Std | Polysee docs | missing | 1 0 1 1 1 1 2 2 2 1 9 6 5 3 1 44 24 16 10 4 1 265 120 65 38 17 5 1 1854 720 326 168 78 26 6 1 14833 |
| Std | PolyRow1∑ k=0..1 T(1, k) n^k | A000027 | 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 35 |
| Std | PolyRow2∑ k=0..2 T(2, k) n^k | A002522 | 1 2 5 10 17 26 37 50 65 82 101 122 145 170 197 226 257 290 325 362 401 442 485 530 577 626 677 730 |
| Std | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 2 6 16 38 78 142 236 366 538 758 1032 1366 1766 2238 2788 3422 4146 4966 5888 6918 8062 9326 10716 |
| Std | PolyCol2∑ k=0..n T(n, k) 2^k | A000522 | 1 2 5 16 65 326 1957 13700 109601 986410 9864101 108505112 1302061345 16926797486 236975164805 |
| Std | PolyCol3∑ k=0..n T(n, k) 3^k | A010842 | 1 3 10 38 168 872 5296 37200 297856 2681216 26813184 294947072 3539368960 46011804672 644165281792 |
| Std | PolyDiag∑ k=0..n T(n, k) n^k | A217701 | 1 1 5 38 393 5144 81445 1512720 32237681 775193984 20759213061 612623724800 19751688891385 |
| Alt | TriangleT(n, k), 0 ≤ k ≤ n | A008290 | 1 0 -1 1 0 1 2 -3 0 -1 9 -8 6 0 1 44 -45 20 -10 0 -1 265 -264 135 -40 15 0 1 1854 -1855 924 -315 70 |
| Alt | RevT(n, n - k), 0 ≤ k ≤ n | A098825 | 1 -1 0 1 0 1 -1 0 -3 2 1 0 6 -8 9 -1 0 -10 20 -45 44 1 0 15 -40 135 -264 265 -1 0 -21 70 -315 924 |
| Alt | InvT-1(n, k), 0 ≤ k ≤ n | missing | 1 0 1 -1 0 1 -2 3 0 1 -3 8 -6 0 1 -44 75 -20 10 0 1 -165 264 -45 40 -15 0 1 -2274 3815 -924 525 -70 |
| Alt | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 0 1 0 -1 1 0 3 -2 1 0 -6 8 -3 1 0 10 -20 75 -44 1 0 -15 40 -45 264 -165 1 0 21 -70 525 -924 |
| Alt | Accsee docs | missing | 1 0 -1 1 1 2 2 -1 -1 -2 9 1 7 7 8 44 -1 19 9 9 8 265 1 136 96 111 111 112 1854 -1 923 608 678 657 |
| Alt | AccRevsee docs | missing | 1 -1 -1 1 1 2 -1 -1 -4 -2 1 1 7 -1 8 -1 -1 -11 9 -36 8 1 1 16 -24 111 -153 112 -1 -1 -22 48 -267 |
| Alt | AntiDiagsee docs | missing | 1 0 1 -1 2 0 9 -3 1 44 -8 0 265 -45 6 -1 1854 -264 20 0 14833 -1855 135 -10 1 133496 -14832 924 -40 |
| Alt | Diffx1T(n, k) (k+1) | missing | 1 0 -2 1 0 3 2 -6 0 -4 9 -16 18 0 5 44 -90 60 -40 0 -6 265 -528 405 -160 75 0 7 1854 -3710 2772 |
| Alt | RowSum∑ k=0..n T(n, k) | A000023 | 1 -1 2 -2 8 8 112 656 5504 49024 491264 5401856 64826368 842734592 11798300672 176974477312 |
| Alt | EvenSum∑ k=0..n T(n, k) even(k) | A062282 | 1 0 2 2 16 64 416 2848 22912 205952 2060032 22659328 271913984 3534877696 49488295936 742324422656 |
| Alt | OddSum∑ k=0..n T(n, k) odd(k) | A063083 | 0 -1 0 -4 -8 -56 -304 -2192 -17408 -156928 -1568768 -17257472 -207087616 -2692143104 -37689995264 |
| Alt | AltSum∑ k=0..n T(n, k) (-1)^k | A000142 | 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 |
| Alt | AbsSum∑ k=0..n | T(n, k) | | A000142 | 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 |
| Alt | DiagSum∑ k=0..n // 2 T(n - k, k) | A177258 | 1 0 0 2 7 36 225 1610 13104 119548 1208583 13413960 162176105 2121703324 29866022640 450112042926 |
| Alt | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 -1 4 -2 32 88 832 6032 54784 539776 5894144 70226176 907565056 12641027072 188772794368 |
| Alt | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A000079 | 1 -2 4 -8 16 -32 64 -128 256 -512 1024 -2048 4096 -8192 16384 -32768 65536 -131072 262144 -524288 |
| Alt | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 1 6 72 1980 629640 75661740 1282617816480 4377895262100360 721520918146760331600 |
| Alt | 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 |
| Alt | RowMaxMax k=0..n | T(n, k) | | A174318 | 1 1 1 3 9 45 265 1855 14833 133497 1334961 14684571 176214841 2290792933 32071101049 481066515735 |
| Alt | ColMiddleT(n, n // 2) | missing | 1 0 0 -3 6 20 -40 -315 630 5544 -11088 -122430 244860 3181464 -6362928 -95450355 190900710 |
| Alt | CentralET(2 n, n) | A281262 | 1 0 6 -40 630 -11088 244860 -6362928 190900710 -6490575520 246642054516 -10358965584240 |
| Alt | CentralOT(2 n + 1, n) | missing | 0 -3 20 -315 5544 -122430 3181464 -95450355 3245287760 -123321027258 5179482792120 -238256209789598 |
| Alt | ColLeftT(n, 0) | A000166 | 1 0 1 2 9 44 265 1854 14833 133496 1334961 14684570 176214841 2290792932 32071101049 481066515734 |
| Alt | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 -1 2 -8 14 -82 132 -744 4566 33442 587036 6952064 87792652 1082005052 13392493064 162520998480 |
| Alt | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -1 2 -12 78 -570 4900 -48160 530390 -6464430 86327388 -1252761048 19620649356 -329739285876 |
| Alt | TransNat0∑ k=0..n T(n, k) k | A335111 | 0 -1 2 -6 8 -40 -48 -784 -5248 -49536 -490240 -5403904 -64822272 -842742784 -11798284288 |
| Alt | TransNat1∑ k=0..n T(n, k) (k + 1) | A000079 | 1 -2 4 -8 16 -32 64 -128 256 -512 1024 -2048 4096 -8192 16384 -32768 65536 -131072 262144 -524288 |
| Alt | TransSqrs∑ k=0..n T(n, k) k^2 | A001787 | 0 -1 4 -12 32 -80 192 -448 1024 -2304 5120 -11264 24576 -53248 114688 -245760 524288 -1114112 |
| Alt | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A343582 | 1 -1 5 3 105 807 10413 143595 2304081 41453775 829134549 18240782931 437779321785 11382260772087 |
| Alt | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A000354 | 1 -1 5 -29 233 -2329 27949 -391285 6260561 -112690097 2253801941 -49583642701 1190007424825 |
| Alt | DiagRow2T(n + 2, 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 |
| Alt | DiagRow3T(n + 3, n) | A007290 | 2 -8 20 -40 70 -112 168 -240 330 -440 572 -728 910 -1120 1360 -1632 1938 -2280 2660 -3080 3542 |
| Alt | DiagCol1T(n + 1, 1) | A000240 | -1 0 -3 -8 -45 -264 -1855 -14832 -133497 -1334960 -14684571 -176214840 -2290792933 -32071101048 |
| Alt | DiagCol2T(n + 2, 2) | A000387 | 1 0 6 20 135 924 7420 66744 667485 7342280 88107426 1145396460 16035550531 240533257860 |
| Alt | DiagCol3T(n + 3, 3) | A000449 | -1 0 -10 -40 -315 -2464 -22260 -222480 -2447445 -29369120 -381798846 -5345183480 -80177752655 |
| Alt | Polysee docs | missing | 1 0 1 1 -1 1 2 2 -2 1 9 -2 5 -3 1 44 8 -12 10 -4 1 265 8 33 -34 17 -5 1 1854 112 -78 120 -74 26 -6 |
| Alt | PolyRow1∑ k=0..1 T(1, k) n^k | A000027 | 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 | A002522 | 1 2 5 10 17 26 37 50 65 82 101 122 145 170 197 226 257 290 325 362 401 442 485 530 577 626 677 730 |
| Alt | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 2 -2 -12 -34 -74 -138 -232 -362 -534 -754 -1028 -1362 -1762 -2234 -2784 -3418 -4142 -4962 -5884 |
| Alt | PolyCol2∑ k=0..n T(n, k) 2^k | A010843 | 1 -2 5 -12 33 -78 261 -360 3681 13446 193509 1951452 23948865 309740922 4341155877 65102989248 |
| Alt | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 -3 10 -34 120 -424 1552 -5520 21376 -69760 350976 -333568 12774400 98958336 1653852160 |
| Alt | PolyDiag∑ k=0..n T(n, k) n^k | A133297 | 1 -1 5 -34 329 -4056 60997 -1082320 22137201 -512801920 13269953861 -379400765184 11877265764025 |
| Rev | TriangleT(n, k), 0 ≤ k ≤ n | A098825 | 1 1 0 1 0 1 1 0 3 2 1 0 6 8 9 1 0 10 20 45 44 1 0 15 40 135 264 265 1 0 21 70 315 924 1855 1854 1 0 |
| Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A055137 | 1 0 1 -1 0 1 -2 -3 0 1 -3 -8 -6 0 1 -4 -15 -20 -10 0 1 -5 -24 -45 -40 -15 0 1 -6 -35 -84 -105 -70 |
| Rev | Accsee docs | missing | 1 1 1 1 1 2 1 1 4 6 1 1 7 15 24 1 1 11 31 76 120 1 1 16 56 191 455 720 1 1 22 92 407 1331 3186 5040 |
| Rev | AccRevsee docs | missing | 1 0 1 1 1 2 2 5 5 6 9 17 23 23 24 44 89 109 119 119 120 265 529 664 704 719 719 720 1854 3709 4633 |
| Rev | AntiDiagsee docs | A371995 | 1 1 1 0 1 0 1 0 1 1 0 3 1 0 6 2 1 0 10 8 1 0 15 20 9 1 0 21 40 45 1 0 28 70 135 44 1 0 36 112 315 |
| Rev | Diffx1T(n, k) (k+1) | missing | 1 1 0 1 0 3 1 0 9 8 1 0 18 32 45 1 0 30 80 225 264 1 0 45 160 675 1584 1855 1 0 63 280 1575 5544 |
| Rev | RowSum∑ k=0..n T(n, k) | A000142 | 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 |
| Rev | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 1 2 4 16 56 416 2192 22912 156928 2060032 17257472 271913984 2692143104 49488295936 565349945344 |
| Rev | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 0 0 2 8 64 304 2848 17408 205952 1568768 22659328 207087616 3534877696 37689995264 742324422656 |
| Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A000023 | 1 1 2 2 8 -8 112 -656 5504 -49024 491264 -5401856 64826368 -842734592 11798300672 -176974477312 |
| Rev | AbsSum∑ k=0..n | T(n, k) | | A000142 | 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 |
| Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | A372102 | 1 1 1 1 2 4 9 19 45 107 278 728 2033 5749 17105 51669 162674 520524 1724329 5807143 20146861 |
| Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A052849 | 1 2 4 12 48 240 1440 10080 80640 725760 7257600 79833600 958003200 12454041600 174356582400 |
| Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A001563 | 1 1 4 18 96 600 4320 35280 322560 3265920 36288000 439084800 5748019200 80951270400 1220496076800 |
| Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 1 6 72 1980 629640 75661740 1282617816480 4377895262100360 721520918146760331600 |
| 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 |
| Rev | RowMaxMax k=0..n | T(n, k) | | A174318 | 1 1 1 3 9 45 265 1855 14833 133497 1334961 14684571 176214841 2290792933 32071101049 481066515735 |
| Rev | ColMiddleT(n, n // 2) | missing | 1 1 0 0 6 10 40 70 630 1134 11088 20328 244860 454740 6362928 11930490 190900710 360590230 |
| Rev | CentralET(2 n, n) | A281262 | 1 0 6 40 630 11088 244860 6362928 190900710 6490575520 246642054516 10358965584240 476512419579196 |
| Rev | CentralOT(2 n + 1, n) | missing | 1 0 10 70 1134 20328 454740 11930490 360590230 12332093488 470862104076 19854684036460 |
| 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) | A000166 | 1 0 1 2 9 44 265 1854 14833 133496 1334961 14684570 176214841 2290792932 32071101049 481066515734 |
| Rev | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 1 2 12 78 570 4900 48160 530390 6464430 86327388 1252761048 19620649356 329739285876 |
| Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -1 2 -8 14 -82 132 -744 4566 33442 587036 6952064 87792652 1082005052 13392493064 162520998480 |
| Rev | TransNat0∑ k=0..n T(n, k) k | A062119 | 0 0 2 12 72 480 3600 30240 282240 2903040 32659200 399168000 5269017600 74724249600 1133317785600 |
| Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | A001563 | 1 1 4 18 96 600 4320 35280 322560 3265920 36288000 439084800 5748019200 80951270400 1220496076800 |
| Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 0 4 30 240 2040 18720 186480 2016000 23587200 297561600 4031596800 58438195200 902918016000 |
| Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A000522 | 1 2 5 16 65 326 1957 13700 109601 986410 9864101 108505112 1302061345 16926797486 236975164805 |
| Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A010843 | 1 -2 5 -12 33 -78 261 -360 3681 13446 193509 1951452 23948865 309740922 4341155877 65102989248 |
| Rev | DiagRow1T(n + 1, n) | A000240 | 1 0 3 8 45 264 1855 14832 133497 1334960 14684571 176214840 2290792933 32071101048 481066515735 |
| Rev | DiagRow2T(n + 2, n) | A000387 | 1 0 6 20 135 924 7420 66744 667485 7342280 88107426 1145396460 16035550531 240533257860 |
| Rev | DiagRow3T(n + 3, n) | A000449 | 1 0 10 40 315 2464 22260 222480 2447445 29369120 381798846 5345183480 80177752655 1282844041920 |
| Rev | DiagCol2T(n + 2, 2) | 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 | DiagCol3T(n + 3, 3) | A007290 | 2 8 20 40 70 112 168 240 330 440 572 728 910 1120 1360 1632 1938 2280 2660 3080 3542 4048 4600 5200 |
| Rev | Polysee docs | missing | 1 1 1 1 1 1 1 2 1 1 1 6 5 1 1 1 24 29 10 1 1 1 120 233 82 17 1 1 1 720 2329 1000 177 26 1 1 1 5040 |
| Rev | PolyRow1∑ k=0..1 T(1, k) n^k | 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 | PolyRow2∑ k=0..2 T(2, k) n^k | A002522 | 1 2 5 10 17 26 37 50 65 82 101 122 145 170 197 226 257 290 325 362 401 442 485 530 577 626 677 730 |
| Rev | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 1 6 29 82 177 326 541 834 1217 1702 2301 3026 3889 4902 6077 7426 8961 10694 12637 14802 17201 |
| Rev | PolyCol2∑ k=0..n T(n, k) 2^k | A000354 | 1 1 5 29 233 2329 27949 391285 6260561 112690097 2253801941 49583642701 1190007424825 |
| Rev | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 1 10 82 1000 14968 269488 5659120 135819136 3667116160 110013485824 3630445030144 130696021089280 |
| Rev | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 1 5 82 2913 168376 14600845 1761398640 281989891841 57797093005696 14753600077944501 |
| Inv | TriangleT(n, k), 0 ≤ k ≤ n | A055137 | 1 0 1 -1 0 1 -2 -3 0 1 -3 -8 -6 0 1 -4 -15 -20 -10 0 1 -5 -24 -45 -40 -15 0 1 -6 -35 -84 -105 -70 |
| Inv | RevT(n, n - k), 0 ≤ k ≤ n | missing | 1 1 0 1 0 -1 1 0 -3 -2 1 0 -6 -8 -3 1 0 -10 -20 -15 -4 1 0 -15 -40 -45 -24 -5 1 0 -21 -70 -105 -84 |
| Inv | RevInvT-1(n, n - k), 0 ≤ k ≤ n | A098825 | 1 1 0 1 0 1 1 0 3 2 1 0 6 8 9 1 0 10 20 45 44 1 0 15 40 135 264 265 1 0 21 70 315 924 1855 1854 1 0 |
| Inv | Accsee docs | missing | 1 0 1 -1 -1 0 -2 -5 -5 -4 -3 -11 -17 -17 -16 -4 -19 -39 -49 -49 -48 -5 -29 -74 -114 -129 -129 -128 |
| Inv | AccRevsee docs | missing | 1 1 1 1 1 0 1 1 -2 -4 1 1 -5 -13 -16 1 1 -9 -29 -44 -48 1 1 -14 -54 -99 -123 -128 1 1 -20 -90 -195 |
| Inv | AntiDiagsee docs | missing | 1 0 -1 1 -2 0 -3 -3 1 -4 -8 0 -5 -15 -6 1 -6 -24 -20 0 -7 -35 -45 -10 1 -8 -48 -84 -40 0 -9 -63 |
| Inv | Diffx1T(n, k) (k+1) | missing | 1 0 2 -1 0 3 -2 -6 0 4 -3 -16 -18 0 5 -4 -30 -60 -40 0 6 -5 -48 -135 -160 -75 0 7 -6 -70 -252 -420 |
| Inv | RowSum∑ k=0..n T(n, k) | A058922 | 1 1 0 -4 -16 -48 -128 -320 -768 -1792 -4096 -9216 -20480 -45056 -98304 -212992 -458752 -983040 |
| Inv | EvenSum∑ k=0..n T(n, k) even(k) | A036289 | 1 0 0 -2 -8 -24 -64 -160 -384 -896 -2048 -4608 -10240 -22528 -49152 -106496 -229376 -491520 |
| Inv | OddSum∑ k=0..n T(n, k) odd(k) | A036289 | 0 1 0 -2 -8 -24 -64 -160 -384 -896 -2048 -4608 -10240 -22528 -49152 -106496 -229376 -491520 |
| Inv | AbsSum∑ k=0..n | T(n, k) | | A048495 | 1 1 2 6 18 50 130 322 770 1794 4098 9218 20482 45058 98306 212994 458754 983042 2097154 4456450 |
| Inv | DiagSum∑ k=0..n // 2 T(n - k, k) | A067331 | 1 0 0 -2 -5 -12 -25 -50 -96 -180 -331 -600 -1075 -1908 -3360 -5878 -10225 -17700 -30509 -52390 |
| Inv | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A076616 | 1 1 -2 -16 -64 -208 -608 -1664 -4352 -11008 -27136 -65536 -155648 -364544 -843776 -1933312 -4390912 |
| Inv | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 2 2 -4 -32 -128 -416 -1216 -3328 -8704 -22016 -54272 -131072 -311296 -729088 -1687552 -3866624 |
| Inv | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 1 6 24 60 360 420 3360 7560 25200 27720 332640 360360 5045040 5405400 5765760 12252240 |
| 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) | | A191522 | 1 1 1 3 8 20 45 105 224 504 1050 2310 4752 10296 21021 45045 91520 194480 393822 831402 1679600 |
| Inv | ColMiddleT(n, n // 2) | missing | 1 0 0 -3 -6 -20 -40 -105 -210 -504 -1008 -2310 -4620 -10296 -20592 -45045 -90090 -194480 -388960 |
| Inv | CentralET(2 n, n) | missing | 1 0 -6 -40 -210 -1008 -4620 -20592 -90090 -388960 -1662804 -7054320 -29745716 -124807200 -521515800 |
| Inv | CentralOT(2 n + 1, n) | A000917 | 0 -3 -20 -105 -504 -2310 -10296 -45045 -194480 -831402 -3527160 -14872858 -62403600 -260757900 |
| Inv | ColLeftT(n, 0) | 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 | 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 1 0 -10 -70 -378 -1848 -8580 -38610 -170170 -739024 -3174444 -13520780 -57203300 -240699600 |
| Inv | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 1 0 -6 -6 30 40 -140 -210 630 1008 -2772 -4620 12012 20592 -51480 -90090 218790 388960 -923780 |
| Inv | TransNat0∑ k=0..n T(n, k) k | A178987 | 0 1 2 0 -16 -80 -288 -896 -2560 -6912 -17920 -45056 -110592 -266240 -630784 -1474560 -3407872 |
| Inv | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 2 2 -4 -32 -128 -416 -1216 -3328 -8704 -22016 -54272 -131072 -311296 -729088 -1687552 -3866624 |
| Inv | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 4 6 -16 -160 -768 -2912 -9728 -29952 -87040 -242176 -651264 -1703936 -4358144 -10936320 |
| Inv | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 1 -3 -27 -135 -567 -2187 -8019 -28431 -98415 -334611 -1121931 -3720087 -12223143 -39858075 |
| Inv | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A005408 | 1 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 |
| Inv | DiagRow2T(n + 2, 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 |
| Inv | DiagRow3T(n + 3, n) | A007290 | -2 -8 -20 -40 -70 -112 -168 -240 -330 -440 -572 -728 -910 -1120 -1360 -1632 -1938 -2280 -2660 -3080 |
| Inv | DiagCol1T(n + 1, 1) | A005563 | 1 0 -3 -8 -15 -24 -35 -48 -63 -80 -99 -120 -143 -168 -195 -224 -255 -288 -323 -360 -399 -440 -483 |
| Inv | DiagCol2T(n + 2, 2) | A005564 | 1 0 -6 -20 -45 -84 -140 -216 -315 -440 -594 -780 -1001 -1260 -1560 -1904 -2295 -2736 -3230 -3780 |
| Inv | DiagCol3T(n + 3, 3) | missing | 1 0 -10 -40 -105 -224 -420 -720 -1155 -1760 -2574 -3640 -5005 -6720 -8840 -11424 -14535 -18240 |
| Inv | Polysee docs | missing | 1 0 1 -1 1 1 -2 0 2 1 -3 -4 3 3 1 -4 -16 0 8 4 1 -5 -48 -27 16 15 5 1 -6 -128 -162 0 50 24 6 1 -7 |
| Inv | PolyRow1∑ k=0..1 T(1, k) n^k | A000027 | 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 35 |
| Inv | PolyRow2∑ k=0..2 T(2, k) n^k | A005563 | -1 0 3 8 15 24 35 48 63 80 99 120 143 168 195 224 255 288 323 360 399 440 483 528 575 624 675 728 |
| Inv | PolyRow3∑ k=0..3 T(3, k) n^k | missing | -2 -4 0 16 50 108 196 320 486 700 968 1296 1690 2156 2700 3328 4046 4860 5776 6800 7938 9196 10580 |
| Inv | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 2 3 0 -27 -162 -729 -2916 -10935 -39366 -137781 -472392 -1594323 -5314410 -17537553 -57395628 |
| Inv | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 3 8 16 0 -256 -2048 -12288 -65536 -327680 -1572864 -7340032 -33554432 -150994944 -671088640 |
| Inv | PolyDiag∑ k=0..n T(n, k) n^k | A000272 | 1 1 3 16 125 1296 16807 262144 4782969 100000000 2357947691 61917364224 1792160394037 |
| Inv:Rev | TriangleT(n, k), 0 ≤ k ≤ n | missing | 1 1 0 1 0 -1 1 0 -3 -2 1 0 -6 -8 -3 1 0 -10 -20 -15 -4 1 0 -15 -40 -45 -24 -5 1 0 -21 -70 -105 -84 |
| Inv:Rev | RevT(n, n - k), 0 ≤ k ≤ n | A055137 | 1 0 1 -1 0 1 -2 -3 0 1 -3 -8 -6 0 1 -4 -15 -20 -10 0 1 -5 -24 -45 -40 -15 0 1 -6 -35 -84 -105 -70 |
| Inv:Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A008290 | 1 0 1 1 0 1 2 3 0 1 9 8 6 0 1 44 45 20 10 0 1 265 264 135 40 15 0 1 1854 1855 924 315 70 21 0 1 |
| Inv:Rev | Accsee docs | missing | 1 1 1 1 1 0 1 1 -2 -4 1 1 -5 -13 -16 1 1 -9 -29 -44 -48 1 1 -14 -54 -99 -123 -128 1 1 -20 -90 -195 |
| Inv:Rev | AccRevsee docs | missing | 1 0 1 -1 -1 0 -2 -5 -5 -4 -3 -11 -17 -17 -16 -4 -19 -39 -49 -49 -48 -5 -29 -74 -114 -129 -129 -128 |
| Inv:Rev | AntiDiagsee docs | missing | 1 1 1 0 1 0 1 0 -1 1 0 -3 1 0 -6 -2 1 0 -10 -8 1 0 -15 -20 -3 1 0 -21 -40 -15 1 0 -28 -70 -45 -4 1 |
| Inv:Rev | Diffx1T(n, k) (k+1) | missing | 1 1 0 1 0 -3 1 0 -9 -8 1 0 -18 -32 -15 1 0 -30 -80 -75 -24 1 0 -45 -160 -225 -144 -35 1 0 -63 -280 |
| Inv:Rev | RowSum∑ k=0..n T(n, k) | A058922 | 1 1 0 -4 -16 -48 -128 -320 -768 -1792 -4096 -9216 -20480 -45056 -98304 -212992 -458752 -983040 |
| Inv:Rev | EvenSum∑ k=0..n T(n, k) even(k) | A036289 | 1 1 0 -2 -8 -24 -64 -160 -384 -896 -2048 -4608 -10240 -22528 -49152 -106496 -229376 -491520 |
| Inv:Rev | OddSum∑ k=0..n T(n, k) odd(k) | A036289 | 0 0 0 -2 -8 -24 -64 -160 -384 -896 -2048 -4608 -10240 -22528 -49152 -106496 -229376 -491520 |
| Inv:Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A019590 | 1 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 |
| Inv:Rev | AbsSum∑ k=0..n | T(n, k) | | A048495 | 1 1 2 6 18 50 130 322 770 1794 4098 9218 20482 45058 98306 212994 458754 983042 2097154 4456450 |
| Inv:Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 1 1 0 -2 -7 -17 -37 -75 -146 -276 -511 -931 -1675 -2983 -5268 -9238 -16103 -27925 -48209 -82899 |
| Inv:Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 2 2 -4 -32 -128 -416 -1216 -3328 -8704 -22016 -54272 -131072 -311296 -729088 -1687552 -3866624 |
| Inv:Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A076616 | 1 1 -2 -16 -64 -208 -608 -1664 -4352 -11008 -27136 -65536 -155648 -364544 -843776 -1933312 -4390912 |
| Inv:Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 1 6 24 60 360 420 3360 7560 25200 27720 332640 360360 5045040 5405400 5765760 12252240 |
| 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) | | A191522 | 1 1 1 3 8 20 45 105 224 504 1050 2310 4752 10296 21021 45045 91520 194480 393822 831402 1679600 |
| Inv:Rev | ColMiddleT(n, n // 2) | missing | 1 1 0 0 -6 -10 -40 -70 -210 -378 -1008 -1848 -4620 -8580 -20592 -38610 -90090 -170170 -388960 |
| Inv:Rev | CentralET(2 n, n) | missing | 1 0 -6 -40 -210 -1008 -4620 -20592 -90090 -388960 -1662804 -7054320 -29745716 -124807200 -521515800 |
| Inv:Rev | CentralOT(2 n + 1, n) | missing | 1 0 -10 -70 -378 -1848 -8580 -38610 -170170 -739024 -3174444 -13520780 -57203300 -240699600 |
| 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) | 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 | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 1 0 -10 -70 -378 -1848 -8580 -38610 -170170 -739024 -3174444 -13520780 -57203300 -240699600 |
| Inv:Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -1 0 6 -6 -30 40 140 -210 -630 1008 2772 -4620 -12012 20592 51480 -90090 -218790 388960 923780 |
| Inv:Rev | TransNat0∑ k=0..n T(n, k) k | A001815 | 0 0 -2 -12 -48 -160 -480 -1344 -3584 -9216 -23040 -56320 -135168 -319488 -745472 -1720320 -3932160 |
| Inv:Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | A076616 | 1 1 -2 -16 -64 -208 -608 -1664 -4352 -11008 -27136 -65536 -155648 -364544 -843776 -1933312 -4390912 |
| Inv:Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 0 -4 -30 -144 -560 -1920 -6048 -17920 -50688 -138240 -366080 -946176 -2396160 -5963776 -14622720 |
| Inv:Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 2 3 0 -27 -162 -729 -2916 -10935 -39366 -137781 -472392 -1594323 -5314410 -17537553 -57395628 |
| Inv:Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^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 |
| Inv:Rev | DiagRow1T(n + 1, n) | A005563 | 1 0 -3 -8 -15 -24 -35 -48 -63 -80 -99 -120 -143 -168 -195 -224 -255 -288 -323 -360 -399 -440 -483 |
| Inv:Rev | DiagRow2T(n + 2, n) | A005564 | 1 0 -6 -20 -45 -84 -140 -216 -315 -440 -594 -780 -1001 -1260 -1560 -1904 -2295 -2736 -3230 -3780 |
| Inv:Rev | DiagRow3T(n + 3, n) | missing | 1 0 -10 -40 -105 -224 -420 -720 -1155 -1760 -2574 -3640 -5005 -6720 -8840 -11424 -14535 -18240 |
| Inv:Rev | DiagCol2T(n + 2, 2) | A000217 | -1 -3 -6 -10 -15 -21 -28 -36 -45 -55 -66 -78 -91 -105 -120 -136 -153 -171 -190 -210 -231 -253 -276 |
| Inv:Rev | DiagCol3T(n + 3, 3) | A007290 | -2 -8 -20 -40 -70 -112 -168 -240 -330 -440 -572 -728 -910 -1120 -1360 -1632 -1938 -2280 -2660 -3080 |
| Inv:Rev | Polysee docs | missing | 1 1 1 1 1 1 1 0 1 1 1 -4 -3 1 1 1 -16 -27 -8 1 1 1 -48 -135 -80 -15 1 1 1 -128 -567 -512 -175 -24 1 |
| Inv:Rev | PolyRow1∑ k=0..1 T(1, k) n^k | 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 | PolyRow2∑ k=0..2 T(2, k) n^k | A005563 | 1 0 -3 -8 -15 -24 -35 -48 -63 -80 -99 -120 -143 -168 -195 -224 -255 -288 -323 -360 -399 -440 -483 |
| Inv:Rev | PolyRow3∑ k=0..3 T(3, k) n^k | A015238 | 1 -4 -27 -80 -175 -324 -539 -832 -1215 -1700 -2299 -3024 -3887 -4900 -6075 -7424 -8959 -10692 |
| Inv:Rev | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 1 -3 -27 -135 -567 -2187 -8019 -28431 -98415 -334611 -1121931 -3720087 -12223143 -39858075 |
| Inv:Rev | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 1 -8 -80 -512 -2816 -14336 -69632 -327680 -1507328 -6815744 -30408704 -134217728 -587202560 |
| Inv:Rev | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 1 -3 -80 -1375 -24624 -487403 -10747904 -263063295 -7100000000 -209857344499 -6748992700416 |
| << | 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.