OEIS Similars: A124644, A098474
| ↕ Type | ↕ Trait | ↕ Anum | ↕ Sequence |
|---|---|---|---|
| Std | TriangleT(n, k), 0 ≤ k ≤ n | A098474 | 1 1 1 1 2 2 1 3 6 5 1 4 12 20 14 1 5 20 50 70 42 1 6 30 100 210 252 132 1 7 42 175 490 882 924 429 |
| Std | RevT(n, n - k), 0 ≤ k ≤ n | A124644 | 1 1 1 2 2 1 5 6 3 1 14 20 12 4 1 42 70 50 20 5 1 132 252 210 100 30 6 1 429 924 882 490 175 42 7 1 |
| Std | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | missing | 1 -1 1 0 -2 1 1 0 -3 1 2 4 0 -4 1 -2 10 10 0 -5 1 -28 -12 30 20 0 -6 1 -65 -196 -42 70 35 0 -7 1 |
| Std | Accsee docs | missing | 1 1 2 1 3 5 1 4 10 15 1 5 17 37 51 1 6 26 76 146 188 1 7 37 137 347 599 731 1 8 50 225 715 1597 |
| Std | AccRevsee docs | missing | 1 1 2 2 4 5 5 11 14 15 14 34 46 50 51 42 112 162 182 187 188 132 384 594 694 724 730 731 429 1353 |
| Std | AntiDiagsee docs | missing | 1 1 1 1 1 2 1 3 2 1 4 6 1 5 12 5 1 6 20 20 1 7 30 50 14 1 8 42 100 70 1 9 56 175 210 42 1 10 72 280 |
| Std | Diffx1T(n, k) (k+1) | A098473 | 1 1 2 1 4 6 1 6 18 20 1 8 36 80 70 1 10 60 200 350 252 1 12 90 400 1050 1512 924 1 14 126 700 2450 |
| Std | RowSum∑ k=0..n T(n, k) | A007317 | 1 2 5 15 51 188 731 2950 12235 51822 223191 974427 4302645 19181100 86211885 390248055 1777495635 |
| Std | EvenSum∑ k=0..n T(n, k) even(k) | A098465 | 1 1 3 7 27 91 373 1457 6163 25795 111897 486421 2153429 9584901 43121211 195082479 888861555 |
| Std | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 1 2 8 24 97 358 1493 6072 26027 111294 488006 2149216 9596199 43090674 195165576 888634080 |
| Std | AltSum∑ k=0..n T(n, k) (-1)^k | A005043 | 1 0 1 -1 3 -6 15 -36 91 -232 603 -1585 4213 -11298 30537 -83097 227475 -625992 1730787 -4805595 |
| Std | AbsSum∑ k=0..n | T(n, k) | | A007317 | 1 2 5 15 51 188 731 2950 12235 51822 223191 974427 4302645 19181100 86211885 390248055 1777495635 |
| Std | DiagSum∑ k=0..n // 2 T(n - k, k) | A090344 | 1 1 2 3 6 11 23 47 102 221 493 1105 2516 5763 13328 30995 72556 170655 403351 957135 2279948 |
| Std | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 3 9 30 111 443 1859 8067 35835 161937 741411 3429528 15995769 75115485 354747285 1683426330 |
| Std | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A026375 | 1 3 11 45 195 873 3989 18483 86515 408105 1936881 9238023 44241261 212601015 1024642875 4950790605 |
| Std | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 2 30 420 2100 69300 6306300 1681680 257297040 12221609400 44812567800 883447765200 |
| Std | RowGcdGcd k=0..n | T(n, k) | > 1 | A000034 | 1 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 |
| Std | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 2 6 20 70 252 924 3696 15444 64350 267410 1108536 4803656 21398104 94645460 416024000 |
| Std | ColMiddleT(n, n // 2) | missing | 1 1 2 3 12 20 100 175 980 1764 10584 19404 121968 226512 1472328 2760615 18404100 34763300 |
| Std | CentralET(2 n, n) | A000888 | 1 2 12 100 980 10584 121968 1472328 18404100 236390440 3103161776 41469525552 562496897872 |
| Std | CentralOT(2 n + 1, n) | A000891 | 1 3 20 175 1764 19404 226512 2760615 34763300 449141836 5924217936 79483257308 1081724803600 |
| 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) | A000108 | 1 1 2 5 14 42 132 429 1430 4862 16796 58786 208012 742900 2674440 9694845 35357670 129644790 |
| Std | BinConv∑ k=0..n C(n, k) T(n, k) | A086618 | 1 2 7 33 183 1118 7281 49626 349999 2535078 18758265 141254655 1079364105 8350678170 65298467487 |
| Std | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 0 -1 -5 -9 16 185 624 175 -9080 -47871 -83995 425161 3735720 11542999 -10531717 -280181985 |
| Std | TransNat0∑ k=0..n T(n, k) k | A026376 | 0 1 6 30 144 685 3258 15533 74280 356283 1713690 8263596 39938616 193419915 938430990 4560542550 |
| Std | TransNat1∑ k=0..n T(n, k) (k + 1) | A026375 | 1 3 11 45 195 873 3989 18483 86515 408105 1936881 9238023 44241261 212601015 1024642875 4950790605 |
| Std | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 10 72 456 2705 15438 85925 469976 2538027 13574070 72048966 380100240 1995256887 10430155050 |
| Std | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A064613 | 1 3 10 37 150 654 3012 14445 71398 361114 1859628 9716194 51373180 274352316 1477635912 8016865533 |
| Std | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A001405 | 1 -1 2 -3 6 -10 20 -35 70 -126 252 -462 924 -1716 3432 -6435 12870 -24310 48620 -92378 184756 |
| Std | DiagRow1T(n + 1, n) | A000984 | 1 2 6 20 70 252 924 3432 12870 48620 184756 705432 2704156 10400600 40116600 155117520 601080390 |
| Std | DiagRow2T(n + 2, n) | A092443 | 1 3 12 50 210 882 3696 15444 64350 267410 1108536 4585308 18929092 78004500 320932800 1318498920 |
| Std | DiagRow3T(n + 3, n) | missing | 1 4 20 100 490 2352 11088 51480 235950 1069640 4803656 21398104 94645460 416024000 1818619200 |
| Std | DiagCol1T(n + 1, 1) | 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 | DiagCol2T(n + 2, 2) | A002378 | 2 6 12 20 30 42 56 72 90 110 132 156 182 210 240 272 306 342 380 420 462 506 552 600 650 702 756 |
| Std | DiagCol3T(n + 3, 3) | A134481 | 5 20 50 100 175 280 420 600 825 1100 1430 1820 2275 2800 3400 4080 4845 5700 6650 7700 8855 10120 |
| Std | Polysee docs | missing | 1 1 1 1 2 1 1 5 3 1 1 15 13 4 1 1 51 71 25 5 1 1 188 441 199 41 6 1 1 731 2955 1795 429 61 7 1 1 |
| 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 | A001844 | 1 5 13 25 41 61 85 113 145 181 221 265 313 365 421 481 545 613 685 761 841 925 1013 1105 1201 1301 |
| Std | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 1 15 71 199 429 791 1315 2031 2969 4159 5631 7415 9541 12039 14939 18271 22065 26351 31159 36519 |
| Std | PolyCol2∑ k=0..n T(n, k) 2^k | A162326 | 1 3 13 71 441 2955 20805 151695 1135345 8671763 67320573 529626839 4213228969 33833367963 |
| Std | PolyCol3∑ k=0..n T(n, k) 3^k | A337167 | 1 4 25 199 1795 17422 177463 1870960 20241403 223438852 2506596547 28494103183 327507800725 |
| Std | PolyDiag∑ k=0..n T(n, k) n^k | A338979 | 1 2 13 199 5073 181776 8413021 478070020 32238960193 2517734880838 223558608409101 |
| Alt | TriangleT(n, k), 0 ≤ k ≤ n | A098474 | 1 1 -1 1 -2 2 1 -3 6 -5 1 -4 12 -20 14 1 -5 20 -50 70 -42 1 -6 30 -100 210 -252 132 1 -7 42 -175 |
| Alt | RevT(n, n - k), 0 ≤ k ≤ n | A124644 | 1 -1 1 2 -2 1 -5 6 -3 1 14 -20 12 -4 1 -42 70 -50 20 -5 1 132 -252 210 -100 30 -6 1 -429 924 -882 |
| Alt | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | missing | 1 1 1 0 2 1 -1 0 3 1 2 -4 0 4 1 2 10 -10 0 5 1 -28 12 30 -20 0 6 1 65 -196 42 70 -35 0 7 1 338 520 |
| Alt | Accsee docs | missing | 1 1 0 1 -1 1 1 -2 4 -1 1 -3 9 -11 3 1 -4 16 -34 36 -6 1 -5 25 -75 135 -117 15 1 -6 36 -139 351 -531 |
| Alt | AccRevsee docs | missing | 1 -1 0 2 0 1 -5 1 -2 -1 14 -6 6 2 3 -42 28 -22 -2 -7 -6 132 -120 90 -10 20 14 15 -429 495 -387 103 |
| Alt | AntiDiagsee docs | missing | 1 1 1 -1 1 -2 1 -3 2 1 -4 6 1 -5 12 -5 1 -6 20 -20 1 -7 30 -50 14 1 -8 42 -100 70 1 -9 56 -175 210 |
| Alt | Diffx1T(n, k) (k+1) | A098473 | 1 1 -2 1 -4 6 1 -6 18 -20 1 -8 36 -80 70 1 -10 60 -200 350 -252 1 -12 90 -400 1050 -1512 924 1 -14 |
| Alt | RowSum∑ k=0..n T(n, k) | A005043 | 1 0 1 -1 3 -6 15 -36 91 -232 603 -1585 4213 -11298 30537 -83097 227475 -625992 1730787 -4805595 |
| Alt | EvenSum∑ k=0..n T(n, k) even(k) | A098465 | 1 1 3 7 27 91 373 1457 6163 25795 111897 486421 2153429 9584901 43121211 195082479 888861555 |
| Alt | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 -1 -2 -8 -24 -97 -358 -1493 -6072 -26027 -111294 -488006 -2149216 -9596199 -43090674 -195165576 |
| Alt | AltSum∑ k=0..n T(n, k) (-1)^k | A007317 | 1 2 5 15 51 188 731 2950 12235 51822 223191 974427 4302645 19181100 86211885 390248055 1777495635 |
| Alt | AbsSum∑ k=0..n | T(n, k) | | A007317 | 1 2 5 15 51 188 731 2950 12235 51822 223191 974427 4302645 19181100 86211885 390248055 1777495635 |
| Alt | DiagSum∑ k=0..n // 2 T(n - k, k) | A360024 | 1 1 0 -1 0 3 3 -5 -12 5 41 21 -110 -165 210 735 -30 -2505 -2205 6555 13710 -10035 -57390 -18471 |
| Alt | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 1 1 2 -1 9 -21 69 -197 587 -1717 5048 -14807 43471 -127635 374958 -1102077 3241083 -9537069 |
| Alt | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A002426 | 1 -1 3 -7 19 -51 141 -393 1107 -3139 8953 -25653 73789 -212941 616227 -1787607 5196627 -15134931 |
| Alt | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 2 30 420 2100 69300 6306300 1681680 257297040 12221609400 44812567800 883447765200 |
| Alt | RowGcdGcd k=0..n | T(n, k) | > 1 | A000034 | 1 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 |
| Alt | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 2 6 20 70 252 924 3696 15444 64350 267410 1108536 4803656 21398104 94645460 416024000 |
| Alt | ColMiddleT(n, n // 2) | missing | 1 1 -2 -3 12 20 -100 -175 980 1764 -10584 -19404 121968 226512 -1472328 -2760615 18404100 34763300 |
| Alt | CentralET(2 n, n) | A000888 | 1 -2 12 -100 980 -10584 121968 -1472328 18404100 -236390440 3103161776 -41469525552 562496897872 |
| Alt | CentralOT(2 n + 1, n) | A000891 | 1 -3 20 -175 1764 -19404 226512 -2760615 34763300 -449141836 5924217936 -79483257308 1081724803600 |
| 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 | ColRightT(n, n) | A000108 | 1 -1 2 -5 14 -42 132 -429 1430 -4862 16796 -58786 208012 -742900 2674440 -9694845 35357670 |
| Alt | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 0 -1 5 -9 -16 185 -624 175 9080 -47871 83995 425161 -3735720 11542999 10531717 -280181985 |
| Alt | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A086618 | 1 -2 7 -33 183 -1118 7281 -49626 349999 -2535078 18758265 -141254655 1079364105 -8350678170 |
| Alt | TransNat0∑ k=0..n T(n, k) k | A005717 | 0 -1 2 -6 16 -45 126 -357 1016 -2907 8350 -24068 69576 -201643 585690 -1704510 4969152 -14508939 |
| Alt | TransNat1∑ k=0..n T(n, k) (k + 1) | A002426 | 1 -1 3 -7 19 -51 141 -393 1107 -3139 8953 -25653 73789 -212941 616227 -1787607 5196627 -15134931 |
| Alt | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 -1 6 -24 88 -305 1026 -3381 10984 -35307 112570 -356598 1123728 -3525847 11022662 -34353000 |
| Alt | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A001405 | 1 1 2 3 6 10 20 35 70 126 252 462 924 1716 3432 6435 12870 24310 48620 92378 184756 352716 705432 |
| Alt | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A064613 | 1 -3 10 -37 150 -654 3012 -14445 71398 -361114 1859628 -9716194 51373180 -274352316 1477635912 |
| Alt | DiagRow1T(n + 1, n) | A000984 | 1 -2 6 -20 70 -252 924 -3432 12870 -48620 184756 -705432 2704156 -10400600 40116600 -155117520 |
| Alt | DiagRow2T(n + 2, n) | A092443 | 1 -3 12 -50 210 -882 3696 -15444 64350 -267410 1108536 -4585308 18929092 -78004500 320932800 |
| Alt | DiagRow3T(n + 3, n) | missing | 1 -4 20 -100 490 -2352 11088 -51480 235950 -1069640 4803656 -21398104 94645460 -416024000 |
| Alt | DiagCol1T(n + 1, 1) | 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 |
| Alt | DiagCol2T(n + 2, 2) | A002378 | 2 6 12 20 30 42 56 72 90 110 132 156 182 210 240 272 306 342 380 420 462 506 552 600 650 702 756 |
| Alt | DiagCol3T(n + 3, 3) | A134481 | -5 -20 -50 -100 -175 -280 -420 -600 -825 -1100 -1430 -1820 -2275 -2800 -3400 -4080 -4845 -5700 |
| Alt | Polysee docs | missing | 1 1 1 1 0 1 1 1 -1 1 1 -1 5 -2 1 1 3 -21 13 -3 1 1 -6 105 -89 25 -4 1 1 15 -553 691 -235 41 -5 1 1 |
| 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 | A001844 | 1 1 5 13 25 41 61 85 113 145 181 221 265 313 365 421 481 545 613 685 761 841 925 1013 1105 1201 |
| Alt | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 1 -1 -21 -89 -235 -489 -881 -1441 -2199 -3185 -4429 -5961 -7811 -10009 -12585 -15569 -18991 -22881 |
| Alt | PolyCol2∑ k=0..n T(n, k) 2^k | A337168 | 1 -1 5 -21 105 -553 3053 -17405 101713 -606033 3667797 -22485477 139340985 -871429497 5492959293 |
| Alt | PolyCol3∑ k=0..n T(n, k) 3^k | A337169 | 1 -2 13 -89 691 -5720 49555 -443630 4071595 -38105342 362271823 -3488988101 33967656469 |
| Alt | PolyDiag∑ k=0..n T(n, k) n^k | A339001 | 1 0 5 -89 2481 -93274 4450645 -258297570 17689681345 -1397903887808 125286890408901 |
| Rev | TriangleT(n, k), 0 ≤ k ≤ n | A124644 | 1 1 1 2 2 1 5 6 3 1 14 20 12 4 1 42 70 50 20 5 1 132 252 210 100 30 6 1 429 924 882 490 175 42 7 1 |
| Rev | InvT-1(n, k), 0 ≤ k ≤ n | missing | 1 -1 1 0 -2 1 1 0 -3 1 2 4 0 -4 1 -2 10 10 0 -5 1 -28 -12 30 20 0 -6 1 -65 -196 -42 70 35 0 -7 1 |
| Rev | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 -1 1 -2 0 1 -3 0 1 1 -4 0 4 2 1 -5 0 10 10 -2 1 -6 0 20 30 -12 -28 1 -7 0 35 70 -42 -196 -65 1 |
| Rev | Accsee docs | missing | 1 1 2 2 4 5 5 11 14 15 14 34 46 50 51 42 112 162 182 187 188 132 384 594 694 724 730 731 429 1353 |
| Rev | AccRevsee docs | missing | 1 1 2 1 3 5 1 4 10 15 1 5 17 37 51 1 6 26 76 146 188 1 7 37 137 347 599 731 1 8 50 225 715 1597 |
| Rev | AntiDiagsee docs | missing | 1 1 2 1 5 2 14 6 1 42 20 3 132 70 12 1 429 252 50 4 1430 924 210 20 1 4862 3432 882 100 5 16796 |
| Rev | Diffx1T(n, k) (k+1) | missing | 1 1 2 2 4 3 5 12 9 4 14 40 36 16 5 42 140 150 80 25 6 132 504 630 400 150 36 7 429 1848 2646 1960 |
| Rev | RowSum∑ k=0..n T(n, k) | A007317 | 1 2 5 15 51 188 731 2950 12235 51822 223191 974427 4302645 19181100 86211885 390248055 1777495635 |
| Rev | EvenSum∑ k=0..n T(n, k) even(k) | A102318 | 1 1 3 8 27 97 373 1493 6163 26027 111897 488006 2153429 9596199 43121211 195165576 888861555 |
| Rev | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 1 2 7 24 91 358 1457 6072 25795 111294 486421 2149216 9584901 43090674 195082479 888634080 |
| Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A005043 | 1 0 1 1 3 6 15 36 91 232 603 1585 4213 11298 30537 83097 227475 625992 1730787 4805595 13393689 |
| Rev | AbsSum∑ k=0..n | T(n, k) | | A007317 | 1 2 5 15 51 188 731 2950 12235 51822 223191 974427 4302645 19181100 86211885 390248055 1777495635 |
| Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | A105864 | 1 1 3 7 21 65 215 735 2585 9281 33883 125383 469229 1772801 6752623 25902975 99978865 388001025 |
| Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A026375 | 1 3 11 45 195 873 3989 18483 86515 408105 1936881 9238023 44241261 212601015 1024642875 4950790605 |
| Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 3 9 30 111 443 1859 8067 35835 161937 741411 3429528 15995769 75115485 354747285 1683426330 |
| Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 2 30 420 2100 69300 6306300 1681680 257297040 12221609400 44812567800 883447765200 |
| Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | A000034 | 1 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 |
| Rev | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 2 6 20 70 252 924 3696 15444 64350 267410 1108536 4803656 21398104 94645460 416024000 |
| Rev | ColMiddleT(n, n // 2) | missing | 1 1 2 6 12 50 100 490 980 5292 10584 60984 121968 736164 1472328 9202050 18404100 118195220 |
| Rev | CentralET(2 n, n) | A000888 | 1 2 12 100 980 10584 121968 1472328 18404100 236390440 3103161776 41469525552 562496897872 |
| Rev | CentralOT(2 n + 1, n) | A125558 | 1 6 50 490 5292 60984 736164 9202050 118195220 1551580888 20734762776 281248448936 3863302870000 |
| Rev | ColLeftT(n, 0) | A000108 | 1 1 2 5 14 42 132 429 1430 4862 16796 58786 208012 742900 2674440 9694845 35357670 129644790 |
| 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) | A086618 | 1 2 7 33 183 1118 7281 49626 349999 2535078 18758265 141254655 1079364105 8350678170 65298467487 |
| Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 0 -1 5 -9 -16 185 -624 175 9080 -47871 83995 425161 -3735720 11542999 10531717 -280181985 |
| Rev | TransNat0∑ k=0..n T(n, k) k | missing | 0 1 4 15 60 255 1128 5117 23600 110115 518220 2455101 11693124 55934385 268535400 1293178275 |
| Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 3 9 30 111 443 1859 8067 35835 161937 741411 3429528 15995769 75115485 354747285 1683426330 |
| Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 6 27 120 555 2658 13013 64536 322515 1619370 8155521 41154336 207944997 1051616790 5321209275 |
| Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A162326 | 1 3 13 71 441 2955 20805 151695 1135345 8671763 67320573 529626839 4213228969 33833367963 |
| Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A337168 | 1 -1 5 -21 105 -553 3053 -17405 101713 -606033 3667797 -22485477 139340985 -871429497 5492959293 |
| Rev | DiagRow1T(n + 1, n) | 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 | DiagRow2T(n + 2, n) | A002378 | 2 6 12 20 30 42 56 72 90 110 132 156 182 210 240 272 306 342 380 420 462 506 552 600 650 702 756 |
| Rev | DiagRow3T(n + 3, n) | A134481 | 5 20 50 100 175 280 420 600 825 1100 1430 1820 2275 2800 3400 4080 4845 5700 6650 7700 8855 10120 |
| Rev | DiagCol1T(n + 1, 1) | A000984 | 1 2 6 20 70 252 924 3432 12870 48620 184756 705432 2704156 10400600 40116600 155117520 601080390 |
| Rev | DiagCol2T(n + 2, 2) | A092443 | 1 3 12 50 210 882 3696 15444 64350 267410 1108536 4585308 18929092 78004500 320932800 1318498920 |
| Rev | DiagCol3T(n + 3, 3) | missing | 1 4 20 100 490 2352 11088 51480 235950 1069640 4803656 21398104 94645460 416024000 1818619200 |
| Rev | Polysee docs | A271025 | 1 1 1 2 2 1 5 5 3 1 14 15 10 4 1 42 51 37 17 5 1 132 188 150 77 26 6 1 429 731 654 371 141 37 7 1 |
| 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 | A002522 | 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 | A005491 | 5 15 37 77 141 235 365 537 757 1031 1365 1765 2237 2787 3421 4145 4965 5887 6917 8061 9325 10715 |
| Rev | PolyCol2∑ k=0..n T(n, k) 2^k | A064613 | 1 3 10 37 150 654 3012 14445 71398 361114 1859628 9716194 51373180 274352316 1477635912 8016865533 |
| Rev | PolyCol3∑ k=0..n T(n, k) 3^k | A104455 | 1 4 17 77 371 1890 10095 56040 320795 1881524 11250827 68330773 420314629 2612922694 16389162537 |
| Rev | PolyDiag∑ k=0..n T(n, k) n^k | A292632 | 1 2 10 77 798 10392 162996 2991340 62893270 1490758022 39334017996 1143492521437 36318168041260 |
| Rev:Inv | TriangleT(n, k), 0 ≤ k ≤ n | missing | 1 -1 1 0 -2 1 1 0 -3 1 2 4 0 -4 1 -2 10 10 0 -5 1 -28 -12 30 20 0 -6 1 -65 -196 -42 70 35 0 -7 1 |
| Rev:Inv | RevT(n, n - k), 0 ≤ k ≤ n | missing | 1 1 -1 1 -2 0 1 -3 0 1 1 -4 0 4 2 1 -5 0 10 10 -2 1 -6 0 20 30 -12 -28 1 -7 0 35 70 -42 -196 -65 1 |
| Rev:Inv | InvT-1(n, k), 0 ≤ k ≤ n | A124644 | 1 1 1 2 2 1 5 6 3 1 14 20 12 4 1 42 70 50 20 5 1 132 252 210 100 30 6 1 429 924 882 490 175 42 7 1 |
| Rev:Inv | RevInvT-1(n, n - k), 0 ≤ k ≤ n | A098474 | 1 1 1 1 2 2 1 3 6 5 1 4 12 20 14 1 5 20 50 70 42 1 6 30 100 210 252 132 1 7 42 175 490 882 924 429 |
| Rev:Inv | Accsee docs | missing | 1 -1 0 0 -2 -1 1 1 -2 -1 2 6 6 2 3 -2 8 18 18 13 14 -28 -40 -10 10 10 4 5 -65 -261 -303 -233 -198 |
| Rev:Inv | AccRevsee docs | missing | 1 1 0 1 -1 -1 1 -2 -2 -1 1 -3 -3 1 3 1 -4 -4 6 16 14 1 -5 -5 15 45 33 5 1 -6 -6 29 99 57 -139 -204 |
| Rev:Inv | AntiDiagsee docs | missing | 1 -1 0 1 1 -2 2 0 1 -2 4 -3 -28 10 0 1 -65 -12 10 -4 338 -196 30 0 1 3262 -520 -42 20 -5 4352 3042 |
| Rev:Inv | Diffx1T(n, k) (k+1) | missing | 1 -1 2 0 -4 3 1 0 -9 4 2 8 0 -16 5 -2 20 30 0 -25 6 -28 -24 90 80 0 -36 7 -65 -392 -126 280 175 0 |
| Rev:Inv | RowSum∑ k=0..n T(n, k) | missing | 1 0 -1 -1 3 14 5 -204 -889 1688 38529 135475 -1141679 -15252654 -24899225 1036057855 10337435655 |
| Rev:Inv | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 -1 1 -2 3 3 3 -79 -305 745 14103 44108 -449479 -5456895 -6071335 391343078 3600465159 |
| Rev:Inv | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 1 -2 1 0 11 2 -125 -584 943 24426 91367 -692200 -9795759 -18827890 644714777 6736970496 |
| Rev:Inv | AltSum∑ k=0..n T(n, k) (-1)^k | missing | 1 -2 3 -3 3 -8 1 46 279 -198 -10323 -47259 242721 4338864 12756555 -253371699 -3136505337 262118458 |
| Rev:Inv | AbsSum∑ k=0..n | T(n, k) | | missing | 1 2 3 5 11 28 97 416 1959 11594 66917 432281 3488465 25570128 218050315 2145917987 20678172227 |
| Rev:Inv | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 -1 1 -1 3 -1 -17 -71 173 2715 6681 -82885 -818269 -40565 57549675 417476813 -2124400207 |
| Rev:Inv | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 -1 -3 -1 19 69 -49 -1667 -6369 24881 406939 1201881 -16467527 -198695329 -159951219 16950414055 |
| Rev:Inv | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 1 -1 -4 -1 29 89 -169 -2521 -6313 55409 559294 484021 -30094481 -238436381 662569480 26914361335 |
| Rev:Inv | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 2 3 4 10 420 38220 662480 1389220560 1889339961600 130564097606342400 6887047246178391452160 |
| Rev:Inv | RowGcdGcd k=0..n | T(n, k) | > 1 | missing | 1 1 2 3 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 |
| Rev:Inv | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 2 3 4 10 30 196 784 3262 32620 179410 1356984 11428820 80001740 1029616800 8236934400 |
| Rev:Inv | ColMiddleT(n, n // 2) | missing | 1 -1 -2 0 0 10 20 70 140 -252 -504 -12936 -25872 -111540 -223080 2175030 4350060 79299220 158598440 |
| Rev:Inv | CentralET(2 n, n) | missing | 1 -2 0 20 140 -504 -25872 -223080 4350060 158598440 804058112 -79771661424 -2377331705840 |
| Rev:Inv | CentralOT(2 n + 1, n) | missing | -1 0 10 70 -252 -12936 -111540 2175030 79299220 402029056 -39885830712 -1188665852920 5954405903600 |
| Rev:Inv | ColLeftT(n, 0) | A178955 | 1 -1 0 1 2 -2 -28 -65 338 3262 4352 -113082 -879140 1145012 68641120 409571279 -3075414734 |
| 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 -7 3 124 715 1308 -19173 -244192 -1180305 6246195 177099505 1471962660 -2511097615 |
| Rev:Inv | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 2 5 9 3 -22 131 850 -4453 -32682 264711 1693827 -22137615 -100309986 2404653465 4645440633 |
| Rev:Inv | TransNat0∑ k=0..n T(n, k) k | missing | 0 1 0 -3 -4 15 84 35 -1632 -8001 16880 423819 1625700 -14841827 -213537156 -373488375 16576925680 |
| Rev:Inv | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 1 -1 -4 -1 29 89 -169 -2521 -6313 55409 559294 484021 -30094481 -238436381 662569480 26914361335 |
| Rev:Inv | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 2 -3 -16 -5 174 623 -1352 -22689 -63130 609499 6711528 6292273 -421322734 -3576545715 |
| Rev:Inv | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 -1 -3 3 57 167 -1547 -20821 -31119 1995471 23668461 -80027181 -5683950423 -52934030217 |
| Rev:Inv | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 3 5 -1 9 155 -1075 -2025 108305 -730957 -7707243 204988591 -847330535 -37925156277 751309761373 |
| Rev:Inv | DiagRow1T(n + 1, n) | 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 |
| Rev:Inv | DiagRow3T(n + 3, n) | A000292 | 1 4 10 20 35 56 84 120 165 220 286 364 455 560 680 816 969 1140 1330 1540 1771 2024 2300 2600 2925 |
| Rev:Inv | DiagCol1T(n + 1, 1) | missing | 1 -2 0 4 10 -12 -196 -520 3042 32620 47872 -1356984 -11428820 16030168 1029616800 6553140464 |
| Rev:Inv | DiagCol2T(n + 2, 2) | missing | 1 -3 0 10 30 -42 -784 -2340 15210 179410 287232 -8820396 -80001740 120226260 8236934400 55701693944 |
| Rev:Inv | DiagCol3T(n + 3, 3) | missing | 1 -4 0 20 70 -112 -2352 -7800 55770 717640 1244672 -41161848 -400008700 641206720 46675961600 |
| Rev:Inv | Polysee docs | missing | 1 -1 1 0 0 1 1 -1 1 1 2 -1 0 2 1 -2 3 -3 3 3 1 -28 14 -6 1 8 4 1 -65 5 10 -13 17 15 5 1 338 -204 |
| 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 | A005563 | 0 -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 |
| Rev:Inv | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 1 -1 -3 1 17 51 109 197 321 487 701 969 1297 1691 2157 2701 3329 4047 4861 5777 6801 7939 9197 |
| Rev:Inv | PolyCol2∑ k=0..n T(n, k) 2^k | A308849 | 1 1 0 -3 -6 10 100 175 -1470 -11214 -4032 447678 2813580 -8767044 -254393568 -1156311585 |
| Rev:Inv | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 2 3 1 -13 -44 17 778 2711 -9482 -139411 -349887 4960177 52144964 11871355 -4077541855 |
| Rev:Inv | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 0 0 1 18 298 5300 104550 2297106 55994512 1504851552 44292772665 1418746343740 49168173703374 |
| << | 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.