OEIS Similars: A269945, A008957, A036969
| ↕ Type | ↕ Trait | ↕ Anum | ↕ Sequence |
|---|---|---|---|
| Std | TriangleT(n, k), 0 ≤ k ≤ n | A269945 | 1 0 1 0 1 1 0 1 5 1 0 1 21 14 1 0 1 85 147 30 1 0 1 341 1408 627 55 1 0 1 1365 13013 11440 2002 91 |
| Std | RevT(n, n - k), 0 ≤ k ≤ n | missing | 1 1 0 1 1 0 1 5 1 0 1 14 21 1 0 1 30 147 85 1 0 1 55 627 1408 341 1 0 1 91 2002 11440 13013 1365 1 |
| Std | InvT-1(n, k), 0 ≤ k ≤ n | A269944 | 1 0 1 0 -1 1 0 4 -5 1 0 -36 49 -14 1 0 576 -820 273 -30 1 0 -14400 21076 -7645 1023 -55 1 0 518400 |
| Std | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 0 1 -1 0 1 -5 4 0 1 -14 49 -36 0 1 -30 273 -820 576 0 1 -55 1023 -7645 21076 -14400 0 1 -91 |
| Std | Accsee docs | missing | 1 0 1 0 1 2 0 1 6 7 0 1 22 36 37 0 1 86 233 263 264 0 1 342 1750 2377 2432 2433 0 1 1366 14379 |
| Std | AccRevsee docs | missing | 1 1 1 1 2 2 1 6 7 7 1 15 36 37 37 1 31 178 263 264 264 1 56 683 2091 2432 2433 2433 1 92 2094 13534 |
| Std | AntiDiagsee docs | missing | 1 0 0 1 0 1 0 1 1 0 1 5 0 1 21 1 0 1 85 14 0 1 341 147 1 0 1 1365 1408 30 0 1 5461 13013 627 1 0 1 |
| Std | Diffx1T(n, k) (k+1) | missing | 1 0 2 0 2 3 0 2 15 4 0 2 63 56 5 0 2 255 588 150 6 0 2 1023 5632 3135 330 7 0 2 4095 52052 57200 |
| Std | RowSum∑ k=0..n T(n, k) | A135920 | 1 1 2 7 37 264 2433 27913 386906 6346119 121159373 2655174768 66028903633 1845579100993 |
| Std | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 0 1 5 22 115 969 12896 206793 3528877 64056886 1297918107 30936365281 877631551680 28575272630753 |
| Std | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 1 1 2 15 149 1464 15017 180113 2817242 57102487 1357256661 35092538352 967947549313 |
| Std | AltSum∑ k=0..n T(n, k) (-1)^k | missing | 1 -1 0 3 7 -34 -495 -2121 26680 711635 6954399 -59338554 -4156173071 -90315997633 -356302000656 |
| Std | AbsSum∑ k=0..n | T(n, k) | | A135920 | 1 1 2 7 37 264 2433 27913 386906 6346119 121159373 2655174768 66028903633 1845579100993 |
| Std | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 0 1 1 2 6 23 100 490 2804 19103 151823 1357237 13334473 143393468 1696860119 22160644132 |
| Std | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 1 3 14 96 847 9335 125211 1991467 36918672 787155058 19074645427 520133159613 15828409510565 |
| Std | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 2 5 21 126 1001 10129 126006 1877593 32888637 666757418 15442626557 404271491249 11855277004330 |
| Std | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 1 5 42 24990 12439680 3123120 943260039381660 56022696483932096138220 1035552670984325476824660 |
| Std | RowGcdGcd k=0..n | T(n, k) | > 1 | A128059 | 1 1 1 5 7 1 11 13 1 17 19 1 23 1 1 29 31 1 1 37 1 41 43 1 47 1 1 53 1 1 59 61 1 1 67 1 71 73 1 1 79 |
| Std | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 1 5 21 147 1408 13013 196053 3255330 53157079 1217854704 31306548900 796513723005 |
| Std | ColMiddleT(n, n // 2) | missing | 1 0 1 1 21 85 1408 13013 196053 3255330 46587905 1217854704 16875270660 638816292660 8657594647800 |
| Std | CentralET(2 n, n) | A298851 | 1 1 21 1408 196053 46587905 16875270660 8657594647800 5974284925007685 5336898188553325075 |
| Std | CentralOT(2 n + 1, n) | missing | 0 1 85 13013 3255330 1217854704 638816292660 448016038000965 405183736699184740 |
| Std | ColLeftT(n, 0) | 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 |
| 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 3 19 187 2476 43017 927207 24103963 740949940 26435241416 1079488367112 49893412457605 |
| Std | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 1 -1 -11 67 476 -13975 67803 3944843 -123221396 431500536 109045213608 -4788702631163 |
| Std | TransNat0∑ k=0..n T(n, k) k | missing | 0 1 3 14 89 737 7696 98093 1490687 26542518 545598045 12787451789 338242587616 10009697903337 |
| Std | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 2 5 21 126 1001 10129 126006 1877593 32888637 666757418 15442626557 404271491249 11855277004330 |
| Std | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 5 30 227 2169 25480 358993 5959213 114813254 2534015395 63373728865 1779550197360 |
| Std | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 1 3 15 121 1345 19371 351663 7791217 205355905 6332211795 225296019663 9135078745321 |
| Std | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 1 -1 -5 49 -135 -3441 80899 -776287 -12602319 862026335 -23143053237 125727658321 25455749984041 |
| Std | DiagRow1T(n + 1, n) | A000330 | 0 1 5 14 30 55 91 140 204 285 385 506 650 819 1015 1240 1496 1785 2109 2470 2870 3311 3795 4324 |
| Std | DiagRow2T(n + 2, n) | A060493 | 0 1 21 147 627 2002 5278 12138 25194 48279 86779 148005 241605 380016 578956 857956 1240932 1756797 |
| Std | DiagRow3T(n + 3, n) | A351105 | 0 1 85 1408 11440 61490 251498 846260 2458676 6369275 15047175 32955780 67746900 131969604 |
| Std | DiagCol1T(n + 1, 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 | DiagCol2T(n + 2, 2) | A002450 | 1 5 21 85 341 1365 5461 21845 87381 349525 1398101 5592405 22369621 89478485 357913941 1431655765 |
| Std | DiagCol3T(n + 3, 3) | A002451 | 1 14 147 1408 13013 118482 1071799 9668036 87099705 784246870 7059619931 63542171784 571901915677 |
| Std | Polysee docs | missing | 1 0 1 0 1 1 0 2 2 1 0 7 6 3 1 0 37 30 12 4 1 0 264 214 75 20 5 1 0 2433 2030 651 148 30 6 1 0 27913 |
| 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 | A002378 | 0 2 6 12 20 30 42 56 72 90 110 132 156 182 210 240 272 306 342 380 420 462 506 552 600 650 702 756 |
| Std | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 0 7 30 75 148 255 402 595 840 1143 1510 1947 2460 3055 3738 4515 5392 6375 7470 8683 10020 11487 |
| Std | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 2 6 30 214 2030 24486 362622 6430198 133915022 3224320710 88610897694 2750125115926 |
| Std | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 3 12 75 651 7410 105969 1845291 38230932 925255515 25774036275 816414883626 29109308308401 |
| Std | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 1 6 75 1492 42380 1603338 77175007 4572924232 325372117815 27264269064110 2648780159593458 |
| Alt | TriangleT(n, k), 0 ≤ k ≤ n | A269945 | 1 0 -1 0 -1 1 0 -1 5 -1 0 -1 21 -14 1 0 -1 85 -147 30 -1 0 -1 341 -1408 627 -55 1 0 -1 1365 -13013 |
| Alt | RevT(n, n - k), 0 ≤ k ≤ n | missing | 1 -1 0 1 -1 0 -1 5 -1 0 1 -14 21 -1 0 -1 30 -147 85 -1 0 1 -55 627 -1408 341 -1 0 -1 91 -2002 11440 |
| Alt | InvT-1(n, k), 0 ≤ k ≤ n | missing | 1 0 1 0 1 1 0 -4 -5 1 0 -76 -91 14 1 0 1608 1910 -273 -30 1 0 130120 154726 -22385 -2277 55 1 0 |
| Alt | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 0 1 1 0 1 -5 -4 0 1 14 -91 -76 0 1 -30 -273 1910 1608 0 1 55 -2277 -22385 154726 130120 0 1 -91 |
| Alt | Accsee docs | missing | 1 0 -1 0 -1 0 0 -1 4 3 0 -1 20 6 7 0 -1 84 -63 -33 -34 0 -1 340 -1068 -441 -496 -495 0 -1 1364 |
| Alt | AccRevsee docs | missing | 1 -1 -1 1 0 0 -1 4 3 3 1 -13 8 7 7 -1 29 -118 -33 -34 -34 1 -54 573 -835 -494 -495 -495 -1 90 -1912 |
| Alt | AntiDiagsee docs | missing | 1 0 0 -1 0 -1 0 -1 1 0 -1 5 0 -1 21 -1 0 -1 85 -14 0 -1 341 -147 1 0 -1 1365 -1408 30 0 -1 5461 |
| Alt | Diffx1T(n, k) (k+1) | missing | 1 0 -2 0 -2 3 0 -2 15 -4 0 -2 63 -56 5 0 -2 255 -588 150 -6 0 -2 1023 -5632 3135 -330 7 0 -2 4095 |
| Alt | RowSum∑ k=0..n T(n, k) | missing | 1 -1 0 3 7 -34 -495 -2121 26680 711635 6954399 -59338554 -4156173071 -90315997633 -356302000656 |
| Alt | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 0 1 5 22 115 969 12896 206793 3528877 64056886 1297918107 30936365281 877631551680 28575272630753 |
| Alt | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 -1 -1 -2 -15 -149 -1464 -15017 -180113 -2817242 -57102487 -1357256661 -35092538352 -967947549313 |
| Alt | AltSum∑ k=0..n T(n, k) (-1)^k | A135920 | 1 1 2 7 37 264 2433 27913 386906 6346119 121159373 2655174768 66028903633 1845579100993 |
| Alt | AbsSum∑ k=0..n | T(n, k) | | A135920 | 1 1 2 7 37 264 2433 27913 386906 6346119 121159373 2655174768 66028903633 1845579100993 |
| Alt | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 0 -1 -1 0 4 19 70 194 -14 -6927 -85253 -790367 -6124581 -34272552 35190287 5605670584 |
| Alt | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 -1 -1 6 32 -47 -2161 -16947 77187 4507608 66640382 -65944527 -32451990035 -962484765205 |
| Alt | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 -2 1 9 10 -191 -1799 -2142 189613 3320377 16812406 -705456675 -25734432959 -392255199290 |
| Alt | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 1 5 42 24990 12439680 3123120 943260039381660 56022696483932096138220 1035552670984325476824660 |
| Alt | RowGcdGcd k=0..n | T(n, k) | > 1 | A128059 | 1 1 1 5 7 1 11 13 1 17 19 1 23 1 1 29 31 1 1 37 1 41 43 1 47 1 1 53 1 1 59 61 1 1 67 1 71 73 1 1 79 |
| Alt | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 1 5 21 147 1408 13013 196053 3255330 53157079 1217854704 31306548900 796513723005 |
| Alt | ColMiddleT(n, n // 2) | missing | 1 0 -1 -1 21 85 -1408 -13013 196053 3255330 -46587905 -1217854704 16875270660 638816292660 |
| Alt | CentralET(2 n, n) | A298851 | 1 -1 21 -1408 196053 -46587905 16875270660 -8657594647800 5974284925007685 -5336898188553325075 |
| Alt | CentralOT(2 n + 1, n) | missing | 0 -1 85 -13013 3255330 -1217854704 638816292660 -448016038000965 405183736699184740 |
| Alt | ColLeftT(n, 0) | 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 |
| Alt | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 -1 -1 11 67 -476 -13975 -67803 3944843 123221396 431500536 -109045213608 -4788702631163 |
| Alt | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -1 3 -19 187 -2476 43017 -927207 24103963 -740949940 26435241416 -1079488367112 49893412457605 |
| Alt | TransNat0∑ k=0..n T(n, k) k | missing | 0 -1 1 6 3 -157 -1304 -21 162933 2608742 9858007 -646118121 -21578259888 -301939201657 |
| Alt | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 -2 1 9 10 -191 -1799 -2142 189613 3320377 16812406 -705456675 -25734432959 -392255199290 |
| Alt | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 -1 3 10 -27 -529 -2616 24559 738315 7666034 -52384155 -4215511625 -94472170704 -446617998289 |
| Alt | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 -1 -1 5 49 135 -3441 -80899 -776287 12602319 862026335 23143053237 125727658321 -25455749984041 |
| Alt | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 -1 3 -15 121 -1345 19371 -351663 7791217 -205355905 6332211795 -225296019663 9135078745321 |
| Alt | DiagRow1T(n + 1, n) | A000330 | 0 -1 5 -14 30 -55 91 -140 204 -285 385 -506 650 -819 1015 -1240 1496 -1785 2109 -2470 2870 -3311 |
| Alt | DiagRow2T(n + 2, n) | A060493 | 0 -1 21 -147 627 -2002 5278 -12138 25194 -48279 86779 -148005 241605 -380016 578956 -857956 1240932 |
| Alt | DiagRow3T(n + 3, n) | A351105 | 0 -1 85 -1408 11440 -61490 251498 -846260 2458676 -6369275 15047175 -32955780 67746900 -131969604 |
| Alt | DiagCol1T(n + 1, 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 |
| Alt | DiagCol2T(n + 2, 2) | A002450 | 1 5 21 85 341 1365 5461 21845 87381 349525 1398101 5592405 22369621 89478485 357913941 1431655765 |
| Alt | DiagCol3T(n + 3, 3) | A002451 | -1 -14 -147 -1408 -13013 -118482 -1071799 -9668036 -87099705 -784246870 -7059619931 -63542171784 |
| Alt | Polysee docs | missing | 1 0 1 0 -1 1 0 0 -2 1 0 3 2 -3 1 0 7 10 6 -4 1 0 -34 -14 15 12 -5 1 0 -495 -390 -111 12 20 -6 1 0 |
| 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 | A002378 | 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 |
| Alt | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 0 3 10 15 12 -5 -42 -105 -200 -333 -510 -737 -1020 -1365 -1778 -2265 -2832 -3485 -4230 -5073 -6020 |
| Alt | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 -2 2 10 -14 -390 -1566 26026 563282 2726490 -128928190 -4151857014 -39381610574 1795178726458 |
| Alt | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 -3 6 15 -111 -1020 3201 165237 1336398 -28137873 -1102520055 -10625661156 499303432401 |
| Alt | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 -1 2 15 -308 -630 139710 -694239 -165412552 2223620739 432151992090 -8538608789964 |
| Rev | TriangleT(n, k), 0 ≤ k ≤ n | missing | 1 1 0 1 1 0 1 5 1 0 1 14 21 1 0 1 30 147 85 1 0 1 55 627 1408 341 1 0 1 91 2002 11440 13013 1365 1 |
| Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A269944 | 1 0 1 0 -1 1 0 4 -5 1 0 -36 49 -14 1 0 576 -820 273 -30 1 0 -14400 21076 -7645 1023 -55 1 0 518400 |
| Rev | Accsee docs | missing | 1 1 1 1 2 2 1 6 7 7 1 15 36 37 37 1 31 178 263 264 264 1 56 683 2091 2432 2433 2433 1 92 2094 13534 |
| Rev | AccRevsee docs | missing | 1 0 1 0 1 2 0 1 6 7 0 1 22 36 37 0 1 86 233 263 264 0 1 342 1750 2377 2432 2433 0 1 1366 14379 |
| Rev | AntiDiagsee docs | missing | 1 1 1 0 1 1 1 5 0 1 14 1 1 30 21 0 1 55 147 1 1 91 627 85 0 1 140 2002 1408 1 1 204 5278 11440 341 |
| Rev | Diffx1T(n, k) (k+1) | missing | 1 1 0 1 2 0 1 10 3 0 1 28 63 4 0 1 60 441 340 5 0 1 110 1881 5632 1705 6 0 1 182 6006 45760 65065 |
| Rev | RowSum∑ k=0..n T(n, k) | A135920 | 1 1 2 7 37 264 2433 27913 386906 6346119 121159373 2655174768 66028903633 1845579100993 |
| Rev | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 1 1 2 22 149 969 15017 206793 2817242 64056886 1357256661 30936365281 967947549313 28575272630753 |
| Rev | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 0 1 5 15 115 1464 12896 180113 3528877 57102487 1297918107 35092538352 877631551680 |
| Rev | AltSum∑ k=0..n T(n, k) (-1)^k | missing | 1 1 0 -3 7 34 -495 2121 26680 -711635 6954399 59338554 -4156173071 90315997633 -356302000656 |
| Rev | AbsSum∑ k=0..n | T(n, k) | | A135920 | 1 1 2 7 37 264 2433 27913 386906 6346119 121159373 2655174768 66028903633 1845579100993 |
| Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 1 2 6 16 52 204 804 3552 17264 86928 474496 2746832 16594128 106431776 713006176 4981753088 |
| Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 2 5 21 126 1001 10129 126006 1877593 32888637 666757418 15442626557 404271491249 11855277004330 |
| Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 1 3 14 96 847 9335 125211 1991467 36918672 787155058 19074645427 520133159613 15828409510565 |
| Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 1 5 42 24990 12439680 3123120 943260039381660 56022696483932096138220 1035552670984325476824660 |
| Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | A128059 | 1 1 1 5 7 1 11 13 1 17 19 1 23 1 1 29 31 1 1 37 1 41 43 1 47 1 1 53 1 1 59 61 1 1 67 1 71 73 1 1 79 |
| Rev | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 1 5 21 147 1408 13013 196053 3255330 53157079 1217854704 31306548900 796513723005 |
| Rev | ColMiddleT(n, n // 2) | missing | 1 1 1 5 21 147 1408 11440 196053 1733303 46587905 434928221 16875270660 163648537860 8657594647800 |
| Rev | CentralET(2 n, n) | A298851 | 1 1 21 1408 196053 46587905 16875270660 8657594647800 5974284925007685 5336898188553325075 |
| Rev | CentralOT(2 n + 1, n) | missing | 1 5 147 11440 1733303 434928221 163648537860 86347951359480 60885363603137535 55328004040455578575 |
| 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) | 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 | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 1 3 19 187 2476 43017 927207 24103963 740949940 26435241416 1079488367112 49893412457605 |
| Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -1 -1 11 67 -476 -13975 -67803 3944843 123221396 431500536 -109045213608 -4788702631163 |
| Rev | TransNat0∑ k=0..n T(n, k) k | missing | 0 0 1 7 59 583 6902 97298 1604561 30572553 665995685 16419470659 454104255980 13982830409572 |
| Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 1 3 14 96 847 9335 125211 1991467 36918672 787155058 19074645427 520133159613 15828409510565 |
| Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 0 1 9 107 1399 20716 353428 6870205 151083569 3737991795 103325936435 3169890217728 |
| Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 2 6 30 214 2030 24486 362622 6430198 133915022 3224320710 88610897694 2750125115926 |
| Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 -2 2 10 -14 -390 -1566 26026 563282 2726490 -128928190 -4151857014 -39381610574 1795178726458 |
| Rev | DiagRow1T(n + 1, 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 | DiagRow2T(n + 2, n) | A002450 | 1 5 21 85 341 1365 5461 21845 87381 349525 1398101 5592405 22369621 89478485 357913941 1431655765 |
| Rev | DiagRow3T(n + 3, n) | A002451 | 1 14 147 1408 13013 118482 1071799 9668036 87099705 784246870 7059619931 63542171784 571901915677 |
| Rev | DiagCol1T(n + 1, 1) | A000330 | 0 1 5 14 30 55 91 140 204 285 385 506 650 819 1015 1240 1496 1785 2109 2470 2870 3311 3795 4324 |
| Rev | DiagCol2T(n + 2, 2) | A060493 | 0 1 21 147 627 2002 5278 12138 25194 48279 86779 148005 241605 380016 578956 857956 1240932 1756797 |
| Rev | DiagCol3T(n + 3, 3) | A351105 | 0 1 85 1408 11440 61490 251498 846260 2458676 6369275 15047175 32955780 67746900 131969604 |
| Rev | Polysee docs | missing | 1 1 1 1 1 1 1 2 1 1 1 7 3 1 1 1 37 15 4 1 1 1 264 121 25 5 1 1 1 2433 1345 259 37 6 1 1 1 27913 |
| 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 | 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 | PolyRow3∑ k=0..3 T(3, k) n^k | A082111 | 1 7 15 25 37 51 67 85 105 127 151 177 205 235 267 301 337 375 415 457 501 547 595 645 697 751 807 |
| Rev | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 1 3 15 121 1345 19371 351663 7791217 205355905 6332211795 225296019663 9135078745321 |
| Rev | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 1 4 25 259 3790 71689 1713649 50362828 1767466081 72686534995 3457360455718 187903262545441 |
| Rev | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 1 3 25 457 15076 776743 58326073 6150938593 877905446095 163344050592251 38485600838380158 |
| Inv | TriangleT(n, k), 0 ≤ k ≤ n | A269944 | 1 0 1 0 -1 1 0 4 -5 1 0 -36 49 -14 1 0 576 -820 273 -30 1 0 -14400 21076 -7645 1023 -55 1 0 518400 |
| Inv | RevT(n, n - k), 0 ≤ k ≤ n | missing | 1 1 0 1 -1 0 1 -5 4 0 1 -14 49 -36 0 1 -30 273 -820 576 0 1 -55 1023 -7645 21076 -14400 0 1 -91 |
| Inv | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 0 1 1 0 1 5 1 0 1 14 21 1 0 1 30 147 85 1 0 1 55 627 1408 341 1 0 1 91 2002 11440 13013 1365 1 |
| Inv | Accsee docs | missing | 1 0 1 0 -1 0 0 4 -1 0 0 -36 13 -1 0 0 576 -244 29 -1 0 0 -14400 6676 -969 54 -1 0 0 518400 -254736 |
| Inv | AccRevsee docs | missing | 1 1 1 1 0 0 1 -4 0 0 1 -13 36 0 0 1 -29 244 -576 0 0 1 -54 969 -6676 14400 0 0 1 -90 2913 -41560 |
| Inv | AntiDiagsee docs | missing | 1 0 0 1 0 -1 0 4 1 0 -36 -5 0 576 49 1 0 -14400 -820 -14 0 518400 21076 273 1 0 -25401600 -773136 |
| Inv | Diffx1T(n, k) (k+1) | missing | 1 0 2 0 -2 3 0 8 -15 4 0 -72 147 -56 5 0 1152 -2460 1092 -150 6 0 -28800 63228 -30580 5115 -330 7 0 |
| Inv | RowSum∑ k=0..n T(n, 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 | EvenSum∑ k=0..n T(n, k) even(k) | A051893 | 1 0 1 -5 50 -850 22100 -817700 40885000 -2657525000 217917050000 -22009622050000 2685173890100000 |
| Inv | OddSum∑ k=0..n T(n, k) odd(k) | A051893 | 0 1 -1 5 -50 850 -22100 817700 -40885000 2657525000 -217917050000 22009622050000 -2685173890100000 |
| Inv | AltSum∑ k=0..n T(n, k) (-1)^k | A101686 | 1 -1 2 -10 100 -1700 44200 -1635400 81770000 -5315050000 435834100000 -44019244100000 |
| Inv | AbsSum∑ k=0..n | T(n, k) | | A101686 | 1 1 2 10 100 1700 44200 1635400 81770000 5315050000 435834100000 44019244100000 5370347780200000 |
| Inv | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 0 1 -1 5 -41 626 -15234 539750 -26182411 1664401784 -134180364264 13371968517277 |
| Inv | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A010791 | 1 1 -1 3 -24 360 -8640 302400 -14515200 914457600 -73156608000 7242504192000 -869100503040000 |
| Inv | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A010791 | 1 2 1 -3 24 -360 8640 -302400 14515200 -914457600 73156608000 -7242504192000 869100503040000 |
| Inv | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 1 20 1764 10745280 326939342400 352300447699200 27645512323747439317996800 |
| 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) | | A001819 | 1 1 1 5 49 820 21076 773136 38402064 2483133696 202759531776 20407635072000 2482492033152000 |
| Inv | ColMiddleT(n, n // 2) | missing | 1 0 -1 4 49 -820 -7645 296296 2475473 -173721912 -1367593305 151847872396 1151541572401 |
| Inv | CentralET(2 n, n) | missing | 1 -1 49 -7645 2475473 -1367593305 1151541572401 -1373222414339685 2202549127844351265 |
| Inv | CentralOT(2 n + 1, n) | missing | 0 4 -820 296296 -173721912 151847872396 -185789298737900 303626807076050640 -639475825269193557040 |
| Inv | ColLeftT(n, 0) | 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 | 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 -1 -2 95 -2739 91856 -3730824 178473359 -9415311509 461692419751 -3335691922342 |
| Inv | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 1 3 28 495 13961 571116 31855272 2319026319 213260663683 24152812221571 3300994974112848 |
| Inv | TransNat0∑ k=0..n T(n, k) k | A010791 | 0 1 1 -3 24 -360 8640 -302400 14515200 -914457600 73156608000 -7242504192000 869100503040000 |
| Inv | TransNat1∑ k=0..n T(n, k) (k + 1) | A010791 | 1 2 1 -3 24 -360 8640 -302400 14515200 -914457600 73156608000 -7242504192000 869100503040000 |
| Inv | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 3 -7 50 -702 16128 -547200 25660800 -1587600000 125179084800 -12246416179200 1455084933120000 |
| Inv | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 1 -1 7 -119 3689 -180761 12834031 -1244901007 158102427889 -25454490890129 5065443687135671 |
| Inv | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A277352 | 1 1 3 27 513 16929 863379 63026667 6239640033 804913564257 131200910973891 26371383105752091 |
| Inv | DiagRow1T(n + 1, n) | A000330 | 0 -1 -5 -14 -30 -55 -91 -140 -204 -285 -385 -506 -650 -819 -1015 -1240 -1496 -1785 -2109 -2470 |
| Inv | DiagRow2T(n + 2, n) | A000596 | 0 4 49 273 1023 3003 7462 16422 32946 61446 108031 180895 290745 451269 679644 997084 1429428 |
| Inv | DiagRow3T(n + 3, n) | A000597 | 0 -36 -820 -7645 -44473 -191620 -669188 -1999370 -5293970 -12728936 -28285400 -58856655 -115842675 |
| Inv | DiagCol1T(n + 1, 1) | A001044 | 1 -1 4 -36 576 -14400 518400 -25401600 1625702400 -131681894400 13168189440000 -1593350922240000 |
| Inv | DiagCol2T(n + 2, 2) | A001819 | 1 -5 49 -820 21076 -773136 38402064 -2483133696 202759531776 -20407635072000 2482492033152000 |
| Inv | DiagCol3T(n + 3, 3) | A001820 | 1 -14 273 -7645 296296 -15291640 1017067024 -84865562640 8689315795776 -1071814846360896 |
| Inv | Polysee docs | missing | 1 0 1 0 1 1 0 0 2 1 0 0 2 3 1 0 0 -4 6 4 1 0 0 28 -6 12 5 1 0 0 -392 36 0 20 6 1 0 0 9016 -468 0 20 |
| 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 | A002378 | 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 | missing | 0 0 -4 -6 0 20 60 126 224 360 540 770 1056 1404 1820 2310 2880 3536 4284 5130 6080 7140 8316 9614 |
| Inv | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 2 2 -4 28 -392 9016 -306544 14407568 -893269216 70568268064 -6915690270272 822967142162368 |
| Inv | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 3 6 -6 36 -468 10296 -339768 15629328 -953389008 74364342624 -7213341234528 851174265674304 |
| Inv | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 1 2 -6 0 880 -34200 1183896 -34972672 0 188941053600 -33814757900000 5034578151702528 |
| Inv:Rev | TriangleT(n, k), 0 ≤ k ≤ n | missing | 1 1 0 1 -1 0 1 -5 4 0 1 -14 49 -36 0 1 -30 273 -820 576 0 1 -55 1023 -7645 21076 -14400 0 1 -91 |
| Inv:Rev | RevT(n, n - k), 0 ≤ k ≤ n | A269944 | 1 0 1 0 -1 1 0 4 -5 1 0 -36 49 -14 1 0 576 -820 273 -30 1 0 -14400 21076 -7645 1023 -55 1 0 518400 |
| Inv:Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A269945 | 1 0 1 0 1 1 0 1 5 1 0 1 21 14 1 0 1 85 147 30 1 0 1 341 1408 627 55 1 0 1 1365 13013 11440 2002 91 |
| Inv:Rev | Accsee docs | missing | 1 1 1 1 0 0 1 -4 0 0 1 -13 36 0 0 1 -29 244 -576 0 0 1 -54 969 -6676 14400 0 0 1 -90 2913 -41560 |
| Inv:Rev | AccRevsee docs | missing | 1 0 1 0 -1 0 0 4 -1 0 0 -36 13 -1 0 0 576 -244 29 -1 0 0 -14400 6676 -969 54 -1 0 0 518400 -254736 |
| Inv:Rev | AntiDiagsee docs | missing | 1 1 1 0 1 -1 1 -5 0 1 -14 4 1 -30 49 0 1 -55 273 -36 1 -91 1023 -820 0 1 -140 3003 -7645 576 1 -204 |
| Inv:Rev | Diffx1T(n, k) (k+1) | missing | 1 1 0 1 -2 0 1 -10 12 0 1 -28 147 -144 0 1 -60 819 -3280 2880 0 1 -110 3069 -30580 105380 -86400 0 |
| Inv:Rev | RowSum∑ k=0..n T(n, 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 | EvenSum∑ k=0..n T(n, k) even(k) | A051893 | 1 1 1 5 50 850 22100 817700 40885000 2657525000 217917050000 22009622050000 2685173890100000 |
| Inv:Rev | OddSum∑ k=0..n T(n, k) odd(k) | A051893 | 0 0 -1 -5 -50 -850 -22100 -817700 -40885000 -2657525000 -217917050000 -22009622050000 |
| Inv:Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A101686 | 1 1 2 10 100 1700 44200 1635400 81770000 5315050000 435834100000 44019244100000 5370347780200000 |
| Inv:Rev | AbsSum∑ k=0..n | T(n, k) | | A101686 | 1 1 2 10 100 1700 44200 1635400 81770000 5315050000 435834100000 44019244100000 5370347780200000 |
| Inv:Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 1 0 -4 -9 20 183 113 -4205 -16138 106414 1065711 -1972516 -71563055 -119596359 5224931877 |
| Inv:Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A010791 | 1 2 1 -3 24 -360 8640 -302400 14515200 -914457600 73156608000 -7242504192000 869100503040000 |
| Inv:Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A010791 | 1 1 -1 3 -24 360 -8640 302400 -14515200 914457600 -73156608000 7242504192000 -869100503040000 |
| Inv:Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 1 20 1764 10745280 326939342400 352300447699200 27645512323747439317996800 |
| 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) | | A001819 | 1 1 1 5 49 820 21076 773136 38402064 2483133696 202759531776 20407635072000 2482492033152000 |
| Inv:Rev | ColMiddleT(n, n // 2) | missing | 1 1 -1 -5 49 273 -7645 -44473 2475473 14739153 -1367593305 -8261931405 1151541572401 7026231453265 |
| Inv:Rev | CentralET(2 n, n) | missing | 1 -1 49 -7645 2475473 -1367593305 1151541572401 -1373222414339685 2202549127844351265 |
| Inv:Rev | CentralOT(2 n + 1, n) | A234324 | 1 -5 273 -44473 14739153 -8261931405 7026231453265 -8439654758970225 13611213226804376865 |
| 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) | 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 | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 1 -1 -2 95 -2739 91856 -3730824 178473359 -9415311509 461692419751 -3335691922342 |
| Inv:Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -1 3 -28 495 -13961 571116 -31855272 2319026319 -213260663683 24152812221571 -3300994974112848 |
| Inv:Rev | TransNat0∑ k=0..n T(n, k) k | A010791 | 0 0 -1 3 -24 360 -8640 302400 -14515200 914457600 -73156608000 7242504192000 -869100503040000 |
| Inv:Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | A010791 | 1 1 -1 3 -24 360 -8640 302400 -14515200 914457600 -73156608000 7242504192000 -869100503040000 |
| Inv:Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 0 -1 11 -142 2898 -87552 3686400 -206582400 14872636800 -1337953075200 147088676044800 |
| Inv:Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 2 2 -4 28 -392 9016 -306544 14407568 -893269216 70568268064 -6915690270272 822967142162368 |
| Inv:Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 -2 6 -36 396 -7128 192456 -7313328 372979728 -24616662048 2043182949984 -208404660898368 |
| Inv:Rev | DiagRow1T(n + 1, n) | A001044 | 1 -1 4 -36 576 -14400 518400 -25401600 1625702400 -131681894400 13168189440000 -1593350922240000 |
| Inv:Rev | DiagRow2T(n + 2, n) | A001819 | 1 -5 49 -820 21076 -773136 38402064 -2483133696 202759531776 -20407635072000 2482492033152000 |
| Inv:Rev | DiagRow3T(n + 3, n) | A001820 | 1 -14 273 -7645 296296 -15291640 1017067024 -84865562640 8689315795776 -1071814846360896 |
| Inv:Rev | DiagCol1T(n + 1, 1) | A000330 | 0 -1 -5 -14 -30 -55 -91 -140 -204 -285 -385 -506 -650 -819 -1015 -1240 -1496 -1785 -2109 -2470 |
| Inv:Rev | DiagCol2T(n + 2, 2) | A000596 | 0 4 49 273 1023 3003 7462 16422 32946 61446 108031 180895 290745 451269 679644 997084 1429428 |
| Inv:Rev | DiagCol3T(n + 3, 3) | A000597 | 0 -36 -820 -7645 -44473 -191620 -669188 -1999370 -5293970 -12728936 -28285400 -58856655 -115842675 |
| Inv:Rev | Polysee docs | missing | 1 1 1 1 1 1 1 0 1 1 1 0 -1 1 1 1 0 7 -2 1 1 1 0 -119 22 -3 1 1 1 0 3689 -572 45 -4 1 1 1 0 -180761 |
| 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 | 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 | PolyRow3∑ k=0..3 T(3, k) n^k | A033954 | 1 0 7 22 45 76 115 162 217 280 351 430 517 612 715 826 945 1072 1207 1350 1501 1660 1827 2002 2185 |
| Inv:Rev | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 1 -1 7 -119 3689 -180761 12834031 -1244901007 158102427889 -25454490890129 5065443687135671 |
| Inv:Rev | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 1 -2 22 -572 26884 -1989416 212867512 -31078656752 5936023439632 -1436517672390944 |
| Inv:Rev | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 1 -1 22 -1575 264176 -86274725 48691443816 -43695180133087 58634755379200000 |
| << | 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.