OEIS Similars: A059297, A059298
| ↕ Type | ↕ Trait | ↕ Anum | ↕ Sequence |
|---|---|---|---|
| Std | TriangleT(n, k), 0 ≤ k ≤ n | A059297 | 1 0 1 0 2 1 0 3 6 1 0 4 24 12 1 0 5 80 90 20 1 0 6 240 540 240 30 1 0 7 672 2835 2240 525 42 1 0 8 |
| Std | RevT(n, n - k), 0 ≤ k ≤ n | A059299 | 1 1 0 1 2 0 1 6 3 0 1 12 24 4 0 1 20 90 80 5 0 1 30 240 540 240 6 0 1 42 525 2240 2835 672 7 0 1 56 |
| Std | InvT-1(n, k), 0 ≤ k ≤ n | A137452 | 1 0 1 0 -2 1 0 9 -6 1 0 -64 48 -12 1 0 625 -500 150 -20 1 0 -7776 6480 -2160 360 -30 1 0 117649 |
| Std | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 0 1 -2 0 1 -6 9 0 1 -12 48 -64 0 1 -20 150 -500 625 0 1 -30 360 -2160 6480 -7776 0 1 -42 735 |
| Std | Accsee docs | missing | 1 0 1 0 2 3 0 3 9 10 0 4 28 40 41 0 5 85 175 195 196 0 6 246 786 1026 1056 1057 0 7 679 3514 5754 |
| Std | AccRevsee docs | missing | 1 1 1 1 3 3 1 7 10 10 1 13 37 41 41 1 21 111 191 196 196 1 31 271 811 1051 1057 1057 1 43 568 2808 |
| Std | AntiDiagsee docs | missing | 1 0 0 1 0 2 0 3 1 0 4 6 0 5 24 1 0 6 80 12 0 7 240 90 1 0 8 672 540 20 0 9 1792 2835 240 1 0 10 |
| Std | Diffx1T(n, k) (k+1) | missing | 1 0 2 0 4 3 0 6 18 4 0 8 72 48 5 0 10 240 360 100 6 0 12 720 2160 1200 180 7 0 14 2016 11340 11200 |
| Std | RowSum∑ k=0..n T(n, k) | A000248 | 1 1 3 10 41 196 1057 6322 41393 293608 2237921 18210094 157329097 1436630092 13810863809 |
| Std | EvenSum∑ k=0..n T(n, k) even(k) | A009121 | 1 0 1 6 25 100 481 2954 20721 151848 1146721 9111982 77652169 710421452 6891125697 69961213170 |
| Std | OddSum∑ k=0..n T(n, k) odd(k) | A009565 | 0 1 2 4 16 96 576 3368 20672 141760 1091200 9098112 79676928 726208640 6919738112 69344336896 |
| Std | AltSum∑ k=0..n T(n, k) (-1)^k | A003725 | 1 -1 -1 2 9 4 -95 -414 49 10088 55521 13870 -2024759 -15787188 -28612415 616876274 7476967905 |
| Std | AbsSum∑ k=0..n | T(n, k) | | A000248 | 1 1 3 10 41 196 1057 6322 41393 293608 2237921 18210094 157329097 1436630092 13810863809 |
| Std | DiagSum∑ k=0..n // 2 T(n - k, k) | A360814 | 1 0 1 2 4 10 30 98 338 1240 4877 20496 91213 426678 2090081 10702438 57193760 318283388 1840036058 |
| Std | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 1 5 22 113 656 4177 28876 214993 1711504 14483681 129678044 1223446105 12120448120 125704088161 |
| Std | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 2 7 28 133 716 4279 28022 198937 1518184 12371371 107053178 979161253 9429003260 95269732783 |
| Std | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 2 6 24 720 2160 907200 108864000 137168640000 57610828800000 266162029056000000 |
| Std | RowGcdGcd k=0..n | T(n, k) | > 1 | A000027 | 1 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 | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 2 6 24 90 540 2835 17920 129024 860160 7218750 61875000 502734375 5043886848 50438868480 |
| Std | ColMiddleT(n, n // 2) | missing | 1 0 2 3 24 80 540 2835 17920 129024 787500 7218750 43110144 480370176 2826399576 37096494435 |
| Std | CentralET(2 n, n) | A367271 | 1 2 24 540 17920 787500 43110144 2826399576 215922769920 18836384175180 1847560000000000 |
| Std | CentralOT(2 n + 1, n) | missing | 0 3 80 2835 129024 7218750 480370176 37096494435 3262832967680 322102169395578 35271600000000000 |
| 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) | A367272 | 1 1 5 28 209 1826 18217 203106 2487361 33077566 473318201 7234847126 117435618577 2014339775800 |
| Std | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A367273 | 1 1 -3 -8 81 26 -3815 17494 178241 -2817746 3552201 315952418 -3635118575 -11060115936 782886068497 |
| Std | TransNat0∑ k=0..n T(n, k) k | A185298 | 0 1 4 18 92 520 3222 21700 157544 1224576 10133450 88843084 821832156 7992373168 81458868974 |
| Std | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 2 7 28 133 716 4279 28022 198937 1518184 12371371 107053178 979161253 9429003260 95269732783 |
| Std | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 6 36 224 1480 10452 78736 630464 5347008 47864420 450765304 4452802224 46014422272 496222253828 |
| Std | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A216689 | 1 1 5 25 153 1121 9373 87417 898033 10052353 121492341 1573957529 21729801481 318121178337 |
| Std | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A356819 | 1 1 -3 1 41 -239 229 8401 -87151 324577 3238541 -70271519 601086265 -142860431 -81504662539 |
| Std | DiagRow1T(n + 1, n) | 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 | DiagRow2T(n + 2, n) | missing | 0 3 24 90 240 525 1008 1764 2880 4455 6600 9438 13104 17745 23520 30600 39168 49419 61560 75810 |
| Std | DiagRow3T(n + 3, n) | missing | 0 4 80 540 2240 7000 18144 41160 84480 160380 286000 484484 786240 1230320 1865920 2754000 3969024 |
| 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) | A001788 | 1 6 24 80 240 672 1792 4608 11520 28160 67584 159744 372736 860160 1966080 4456448 10027008 |
| Std | DiagCol3T(n + 3, 3) | A036216 | 1 12 90 540 2835 13608 61236 262440 1082565 4330260 16888014 64481508 241805655 892820880 |
| Std | Polysee docs | missing | 1 0 1 0 1 1 0 3 2 1 0 10 8 3 1 0 41 38 15 4 1 0 196 216 90 24 5 1 0 1057 1402 633 172 35 6 1 0 6322 |
| 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 | A005563 | 0 3 8 15 24 35 48 63 80 99 120 143 168 195 224 255 288 323 360 399 440 483 528 575 624 675 728 783 |
| Std | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 0 10 38 90 172 290 450 658 920 1242 1630 2090 2628 3250 3962 4770 5680 6698 7830 9082 10460 11970 |
| Std | PolyCol2∑ k=0..n T(n, k) 2^k | A275707 | 1 2 8 38 216 1402 10156 80838 698704 6498674 64579284 681642238 7605025720 89318058858 |
| Std | PolyCol3∑ k=0..n T(n, k) 3^k | A355501 | 1 3 15 90 633 5028 44217 424434 4399953 48858984 577372809 7221983838 95192539641 1317190650636 |
| Std | PolyDiag∑ k=0..n T(n, k) n^k | A295623 | 1 1 8 90 1424 28900 716292 20972098 708317248 27108056808 1159375192100 54799938951934 |
| Alt | TriangleT(n, k), 0 ≤ k ≤ n | A059297 | 1 0 -1 0 -2 1 0 -3 6 -1 0 -4 24 -12 1 0 -5 80 -90 20 -1 0 -6 240 -540 240 -30 1 0 -7 672 -2835 2240 |
| Alt | RevT(n, n - k), 0 ≤ k ≤ n | A059299 | 1 -1 0 1 -2 0 -1 6 -3 0 1 -12 24 -4 0 -1 20 -90 80 -5 0 1 -30 240 -540 240 -6 0 -1 42 -525 2240 |
| Alt | InvT-1(n, k), 0 ≤ k ≤ n | missing | 1 0 1 0 2 1 0 -9 -6 1 0 -152 -96 12 1 0 2075 1300 -150 -20 1 0 93396 58560 -6840 -840 30 1 0 |
| Alt | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 0 1 2 0 1 -6 -9 0 1 12 -96 -152 0 1 -20 -150 1300 2075 0 1 30 -840 -6840 58560 93396 0 1 -42 |
| Alt | Accsee docs | missing | 1 0 -1 0 -2 -1 0 -3 3 2 0 -4 20 8 9 0 -5 75 -15 5 4 0 -6 234 -306 -66 -96 -95 0 -7 665 -2170 70 |
| Alt | AccRevsee docs | missing | 1 -1 -1 1 -1 -1 -1 5 2 2 1 -11 13 9 9 -1 19 -71 9 4 4 1 -29 211 -329 -89 -95 -95 -1 41 -484 1756 |
| Alt | AntiDiagsee docs | missing | 1 0 0 -1 0 -2 0 -3 1 0 -4 6 0 -5 24 -1 0 -6 80 -12 0 -7 240 -90 1 0 -8 672 -540 20 0 -9 1792 -2835 |
| Alt | Diffx1T(n, k) (k+1) | missing | 1 0 -2 0 -4 3 0 -6 18 -4 0 -8 72 -48 5 0 -10 240 -360 100 -6 0 -12 720 -2160 1200 -180 7 0 -14 2016 |
| Alt | RowSum∑ k=0..n T(n, k) | A003725 | 1 -1 -1 2 9 4 -95 -414 49 10088 55521 13870 -2024759 -15787188 -28612415 616876274 7476967905 |
| Alt | EvenSum∑ k=0..n T(n, k) even(k) | A009121 | 1 0 1 6 25 100 481 2954 20721 151848 1146721 9111982 77652169 710421452 6891125697 69961213170 |
| Alt | OddSum∑ k=0..n T(n, k) odd(k) | A009565 | 0 -1 -2 -4 -16 -96 -576 -3368 -20672 -141760 -1091200 -9098112 -79676928 -726208640 -6919738112 |
| Alt | AltSum∑ k=0..n T(n, k) (-1)^k | A000248 | 1 1 3 10 41 196 1057 6322 41393 293608 2237921 18210094 157329097 1436630092 13810863809 |
| Alt | AbsSum∑ k=0..n | T(n, k) | | A000248 | 1 1 3 10 41 196 1057 6322 41393 293608 2237921 18210094 157329097 1436630092 13810863809 |
| Alt | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 0 -1 -2 -2 2 18 62 144 144 -813 -6800 -32331 -112226 -232577 466778 8976674 65488020 349371302 |
| Alt | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 -1 -3 2 33 64 -335 -2724 -4655 55952 504801 1179100 -14176679 -173674632 -691456415 4550929124 |
| Alt | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 -2 -1 8 21 -36 -425 -1002 5145 55016 161451 -998790 -14169947 -63133188 233657775 5935967534 |
| Alt | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 2 6 24 720 2160 907200 108864000 137168640000 57610828800000 266162029056000000 |
| Alt | RowGcdGcd k=0..n | T(n, k) | > 1 | A000027 | 1 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 |
| Alt | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 2 6 24 90 540 2835 17920 129024 860160 7218750 61875000 502734375 5043886848 50438868480 |
| Alt | ColMiddleT(n, n // 2) | missing | 1 0 -2 -3 24 80 -540 -2835 17920 129024 -787500 -7218750 43110144 480370176 -2826399576 |
| Alt | CentralET(2 n, n) | A367271 | 1 -2 24 -540 17920 -787500 43110144 -2826399576 215922769920 -18836384175180 1847560000000000 |
| Alt | CentralOT(2 n + 1, n) | missing | 0 -3 80 -2835 129024 -7218750 480370176 -37096494435 3262832967680 -322102169395578 |
| 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) | A367273 | 1 -1 -3 8 81 -26 -3815 -17494 178241 2817746 3552201 -315952418 -3635118575 11060115936 |
| Alt | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A367272 | 1 -1 5 -28 209 -1826 18217 -203106 2487361 -33077566 473318201 -7234847126 117435618577 |
| Alt | TransNat0∑ k=0..n T(n, k) k | missing | 0 -1 0 6 12 -40 -330 -588 5096 44928 105930 -1012660 -12145188 -47346000 262270190 5319091260 |
| Alt | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 -2 -1 8 21 -36 -425 -1002 5145 55016 161451 -998790 -14169947 -63133188 233657775 5935967534 |
| Alt | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 -1 2 12 0 -200 -780 1344 30016 134208 -282780 -8028680 -49398096 26677248 3298301188 30311851080 |
| Alt | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A356819 | 1 -1 -3 -1 41 239 229 -8401 -87151 -324577 3238541 70271519 601086265 142860431 -81504662539 |
| Alt | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A216689 | 1 -1 5 -25 153 -1121 9373 -87417 898033 -10052353 121492341 -1573957529 21729801481 -318121178337 |
| Alt | DiagRow1T(n + 1, n) | 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 |
| Alt | DiagRow2T(n + 2, n) | missing | 0 -3 24 -90 240 -525 1008 -1764 2880 -4455 6600 -9438 13104 -17745 23520 -30600 39168 -49419 61560 |
| Alt | DiagRow3T(n + 3, n) | missing | 0 -4 80 -540 2240 -7000 18144 -41160 84480 -160380 286000 -484484 786240 -1230320 1865920 -2754000 |
| 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) | A001788 | 1 6 24 80 240 672 1792 4608 11520 28160 67584 159744 372736 860160 1966080 4456448 10027008 |
| Alt | DiagCol3T(n + 3, 3) | A036216 | -1 -12 -90 -540 -2835 -13608 -61236 -262440 -1082565 -4330260 -16888014 -64481508 -241805655 |
| Alt | Polysee docs | missing | 1 0 1 0 -1 1 0 -1 -2 1 0 2 0 -3 1 0 9 10 3 -4 1 0 4 8 18 8 -5 1 0 -95 -122 -39 20 15 -6 1 0 -414 |
| 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 | 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 |
| Alt | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 0 2 10 18 20 10 -18 -70 -152 -270 -430 -638 -900 -1222 -1610 -2070 -2608 -3230 -3942 -4750 -5660 |
| Alt | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 -2 0 10 8 -122 -428 1594 18608 26254 -648916 -5081342 3318856 347739286 2495737220 -6457268918 |
| Alt | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 -3 3 18 -39 -348 441 11778 18129 -475416 -3100791 13831518 304225785 884361228 -21201487431 |
| Alt | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 -1 0 18 -144 100 16380 -267246 749504 69401448 -1849688100 11405686270 797088487536 |
| Rev | TriangleT(n, k), 0 ≤ k ≤ n | A059299 | 1 1 0 1 2 0 1 6 3 0 1 12 24 4 0 1 20 90 80 5 0 1 30 240 540 240 6 0 1 42 525 2240 2835 672 7 0 1 56 |
| Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A137452 | 1 0 1 0 -2 1 0 9 -6 1 0 -64 48 -12 1 0 625 -500 150 -20 1 0 -7776 6480 -2160 360 -30 1 0 117649 |
| Rev | Accsee docs | missing | 1 1 1 1 3 3 1 7 10 10 1 13 37 41 41 1 21 111 191 196 196 1 31 271 811 1051 1057 1057 1 43 568 2808 |
| Rev | AccRevsee docs | missing | 1 0 1 0 2 3 0 3 9 10 0 4 28 40 41 0 5 85 175 195 196 0 6 246 786 1026 1056 1057 0 7 679 3514 5754 |
| Rev | AntiDiagsee docs | missing | 1 1 1 0 1 2 1 6 0 1 12 3 1 20 24 0 1 30 90 4 1 42 240 80 0 1 56 525 540 5 1 72 1008 2240 240 0 1 90 |
| Rev | Diffx1T(n, k) (k+1) | missing | 1 1 0 1 4 0 1 12 9 0 1 24 72 16 0 1 40 270 320 25 0 1 60 720 2160 1200 36 0 1 84 1575 8960 14175 |
| Rev | RowSum∑ k=0..n T(n, k) | A000248 | 1 1 3 10 41 196 1057 6322 41393 293608 2237921 18210094 157329097 1436630092 13810863809 |
| Rev | EvenSum∑ k=0..n T(n, k) even(k) | A195509 | 1 1 1 4 25 96 481 3368 20721 141760 1146721 9098112 77652169 726208640 6891125697 69344336896 |
| Rev | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 0 2 6 16 100 576 2954 20672 151848 1091200 9111982 79676928 710421452 6919738112 69961213170 |
| Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A003725 | 1 1 -1 -2 9 -4 -95 414 49 -10088 55521 -13870 -2024759 15787188 -28612415 -616876274 7476967905 |
| Rev | AbsSum∑ k=0..n | T(n, k) | | A000248 | 1 1 3 10 41 196 1057 6322 41393 293608 2237921 18210094 157329097 1436630092 13810863809 |
| Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | A360782 | 1 1 1 3 7 16 45 125 363 1127 3561 11696 39727 138113 494213 1811075 6784115 25985928 101520833 |
| Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 2 7 28 133 716 4279 28022 198937 1518184 12371371 107053178 979161253 9429003260 95269732783 |
| Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 1 5 22 113 656 4177 28876 214993 1711504 14483681 129678044 1223446105 12120448120 125704088161 |
| Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 2 6 24 720 2160 907200 108864000 137168640000 57610828800000 266162029056000000 |
| Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | A000027 | 1 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 |
| Rev | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 2 6 24 90 540 2835 17920 129024 860160 7218750 61875000 502734375 5043886848 50438868480 |
| Rev | ColMiddleT(n, n // 2) | A367274 | 1 1 2 6 24 90 540 2240 17920 78750 787500 3592512 43110144 201885684 2826399576 13495173120 |
| Rev | CentralET(2 n, n) | A367271 | 1 2 24 540 17920 787500 43110144 2826399576 215922769920 18836384175180 1847560000000000 |
| Rev | CentralOT(2 n + 1, n) | missing | 1 6 90 2240 78750 3592512 201885684 13495173120 1046465787510 92378000000000 9148544655566316 |
| 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) | A367272 | 1 1 5 28 209 1826 18217 203106 2487361 33077566 473318201 7234847126 117435618577 2014339775800 |
| Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A367273 | 1 -1 -3 8 81 -26 -3815 -17494 178241 2817746 3552201 -315952418 -3635118575 11060115936 |
| Rev | TransNat0∑ k=0..n T(n, k) k | missing | 0 0 2 12 72 460 3120 22554 173600 1417896 12245760 111467950 1066117008 10683818028 111893224352 |
| Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 1 5 22 113 656 4177 28876 214993 1711504 14483681 129678044 1223446105 12120448120 125704088161 |
| Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 0 2 18 144 1180 9840 84714 758912 7086888 68987520 699638830 7384220448 81003205452 922303229120 |
| Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A275707 | 1 2 8 38 216 1402 10156 80838 698704 6498674 64579284 681642238 7605025720 89318058858 |
| Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 -2 0 10 8 -122 -428 1594 18608 26254 -648916 -5081342 3318856 347739286 2495737220 -6457268918 |
| 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) | A001788 | 1 6 24 80 240 672 1792 4608 11520 28160 67584 159744 372736 860160 1966080 4456448 10027008 |
| Rev | DiagRow3T(n + 3, n) | A036216 | 1 12 90 540 2835 13608 61236 262440 1082565 4330260 16888014 64481508 241805655 892820880 |
| Rev | DiagCol1T(n + 1, 1) | 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 |
| Rev | DiagCol2T(n + 2, 2) | missing | 0 3 24 90 240 525 1008 1764 2880 4455 6600 9438 13104 17745 23520 30600 39168 49419 61560 75810 |
| Rev | DiagCol3T(n + 3, 3) | missing | 0 4 80 540 2240 7000 18144 41160 84480 160380 286000 484484 786240 1230320 1865920 2754000 3969024 |
| Rev | Polysee docs | missing | 1 1 1 1 1 1 1 3 1 1 1 10 5 1 1 1 41 25 7 1 1 1 196 153 46 9 1 1 1 1057 1121 361 73 11 1 1 1 6322 |
| 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 | 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 | PolyRow3∑ k=0..3 T(3, k) n^k | A100536 | 1 10 25 46 73 106 145 190 241 298 361 430 505 586 673 766 865 970 1081 1198 1321 1450 1585 1726 |
| Rev | PolyCol2∑ k=0..n T(n, k) 2^k | A216689 | 1 1 5 25 153 1121 9373 87417 898033 10052353 121492341 1573957529 21729801481 318121178337 |
| Rev | PolyCol3∑ k=0..n T(n, k) 3^k | A356827 | 1 1 7 46 361 3436 37729 463366 6280369 93015352 1491337441 25684077706 472217487625 9221588527204 |
| Rev | PolyDiag∑ k=0..n T(n, k) n^k | A295552 | 1 1 5 46 689 15476 483157 19719022 1009495489 63119450152 4728073048901 417482964953594 |
| Inv | TriangleT(n, k), 0 ≤ k ≤ n | A137452 | 1 0 1 0 -2 1 0 9 -6 1 0 -64 48 -12 1 0 625 -500 150 -20 1 0 -7776 6480 -2160 360 -30 1 0 117649 |
| Inv | RevT(n, n - k), 0 ≤ k ≤ n | missing | 1 1 0 1 -2 0 1 -6 9 0 1 -12 48 -64 0 1 -20 150 -500 625 0 1 -30 360 -2160 6480 -7776 0 1 -42 735 |
| Inv | RevInvT-1(n, n - k), 0 ≤ k ≤ n | A059299 | 1 1 0 1 2 0 1 6 3 0 1 12 24 4 0 1 20 90 80 5 0 1 30 240 540 240 6 0 1 42 525 2240 2835 672 7 0 1 56 |
| Inv | Accsee docs | missing | 1 0 1 0 -2 -1 0 9 3 4 0 -64 -16 -28 -27 0 625 125 275 255 256 0 -7776 -1296 -3456 -3096 -3126 -3125 |
| Inv | AccRevsee docs | missing | 1 1 1 1 -1 -1 1 -5 4 4 1 -11 37 -27 -27 1 -19 131 -369 256 256 1 -29 331 -1829 4651 -3125 -3125 1 |
| Inv | AntiDiagsee docs | missing | 1 0 0 1 0 -2 0 9 1 0 -64 -6 0 625 48 1 0 -7776 -500 -12 0 117649 6480 150 1 0 -2097152 -100842 |
| Inv | Diffx1T(n, k) (k+1) | missing | 1 0 2 0 -4 3 0 18 -18 4 0 -128 144 -48 5 0 1250 -1500 600 -100 6 0 -15552 19440 -8640 1800 -180 7 0 |
| Inv | RowSum∑ k=0..n T(n, k) | A000312 | 1 1 -1 4 -27 256 -3125 46656 -823543 16777216 -387420489 10000000000 -285311670611 8916100448256 |
| Inv | EvenSum∑ k=0..n T(n, k) even(k) | A274278 | 1 0 1 -6 49 -520 6841 -107744 1979713 -41611392 985263601 -25958682112 753424361713 -23888905963520 |
| Inv | OddSum∑ k=0..n T(n, k) odd(k) | A195136 | 0 1 -2 10 -76 776 -9966 154400 -2803256 58388608 -1372684090 35958682112 -1038736032324 |
| Inv | AltSum∑ k=0..n T(n, k) (-1)^k | A000272 | 1 -1 3 -16 125 -1296 16807 -262144 4782969 -100000000 2357947691 -61917364224 1792160394037 |
| Inv | AbsSum∑ k=0..n | T(n, k) | | A000272 | 1 1 3 16 125 1296 16807 262144 4782969 100000000 2357947691 61917364224 1792160394037 |
| Inv | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 0 1 -2 10 -70 674 -8288 124280 -2200174 44918105 -1038958770 26852449045 -766951172304 |
| Inv | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 1 -3 16 -135 1536 -21875 373248 -7411887 167772160 -4261625379 120000000000 -3709051717943 |
| Inv | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A000312 | 1 2 -1 4 -27 256 -3125 46656 -823543 16777216 -387420489 10000000000 -285311670611 8916100448256 |
| Inv | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 2 18 192 7500 38880 7058940 220200960 12053081880 63000000000 65362309994520 286058222714880 |
| Inv | RowGcdGcd k=0..n | T(n, k) | > 1 | A000027 | 1 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 | RowMaxMax k=0..n | T(n, k) | | A000169 | 1 1 2 9 64 625 7776 117649 2097152 43046721 1000000000 25937424601 743008370688 23298085122481 |
| Inv | ColMiddleT(n, n // 2) | missing | 1 0 -2 9 48 -500 -2160 36015 143360 -3306744 -12600000 372027810 1379524608 -49696825464 |
| Inv | CentralET(2 n, n) | A367254 | 1 -2 48 -2160 143360 -12600000 1379524608 -180889572864 27638114549760 -4822114348846080 |
| Inv | CentralOT(2 n + 1, n) | missing | 0 9 -500 36015 -3306744 372027810 -49696825464 7696360546875 -1356645307125680 268283197308856158 |
| 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) | A367257 | 1 1 -3 10 -15 -474 12565 -258572 5136705 -102255290 2019481101 -37521627252 543274535089 |
| Inv | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A367256 | 1 1 5 46 593 9726 192637 4457580 117769409 3492894070 114790042901 4137157889316 162154385331985 |
| Inv | TransNat0∑ k=0..n T(n, k) k | A063524 | 0 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 | TransNat1∑ k=0..n T(n, k) (k + 1) | A000312 | 1 2 -1 4 -27 256 -3125 46656 -823543 16777216 -387420489 10000000000 -285311670611 8916100448256 |
| Inv | TransSqrs∑ k=0..n T(n, k) k^2 | A055541 | 0 1 2 -6 36 -320 3750 -54432 941192 -18874368 430467210 -11000000000 311249095212 -9659108818944 |
| Inv | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A085527 | 1 1 -3 25 -343 6561 -161051 4826809 -170859375 6975757441 -322687697779 16679880978201 |
| Inv | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A052750 | 1 1 5 49 729 14641 371293 11390625 410338673 16983563041 794280046581 41426511213649 |
| Inv | DiagRow1T(n + 1, n) | A002378 | 0 -2 -6 -12 -20 -30 -42 -56 -72 -90 -110 -132 -156 -182 -210 -240 -272 -306 -342 -380 -420 -462 |
| Inv | DiagRow2T(n + 2, n) | missing | 0 9 48 150 360 735 1344 2268 3600 5445 7920 11154 15288 20475 26880 34680 44064 55233 68400 83790 |
| Inv | DiagRow3T(n + 3, n) | missing | 0 -64 -500 -2160 -6860 -17920 -40824 -84000 -159720 -285120 -483340 -784784 -1228500 -1863680 |
| Inv | DiagCol1T(n + 1, 1) | A000169 | 1 -2 9 -64 625 -7776 117649 -2097152 43046721 -1000000000 25937424601 -743008370688 23298085122481 |
| Inv | DiagCol2T(n + 2, 2) | A053506 | 1 -6 48 -500 6480 -100842 1835008 -38263752 900000000 -23579476910 681091006464 -21505924728444 |
| Inv | DiagCol3T(n + 3, 3) | A053507 | 1 -12 150 -2160 36015 -688128 14880348 -360000000 9646149645 -283787919360 9098660462034 |
| Inv | Polysee docs | missing | 1 0 1 0 1 1 0 -1 2 1 0 4 0 3 1 0 -27 2 3 4 1 0 256 -16 0 8 5 1 0 -3125 162 -3 4 15 6 1 0 46656 |
| 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 | 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 |
| Inv | PolyRow3∑ k=0..3 T(3, k) n^k | A366151 | 0 4 2 0 4 20 54 112 200 324 490 704 972 1300 1694 2160 2704 3332 4050 4864 5780 6804 7942 9200 |
| Inv | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 2 0 2 -16 162 -2048 31250 -559872 11529602 -268435456 6973568802 -200000000000 6276856753442 |
| Inv | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 3 3 0 -3 48 -729 12288 -234375 5038848 -121060821 3221225472 -94143178827 3000000000000 |
| Inv | PolyDiag∑ k=0..n T(n, k) 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 | TriangleT(n, k), 0 ≤ k ≤ n | missing | 1 1 0 1 -2 0 1 -6 9 0 1 -12 48 -64 0 1 -20 150 -500 625 0 1 -30 360 -2160 6480 -7776 0 1 -42 735 |
| Inv:Rev | RevT(n, n - k), 0 ≤ k ≤ n | A137452 | 1 0 1 0 -2 1 0 9 -6 1 0 -64 48 -12 1 0 625 -500 150 -20 1 0 -7776 6480 -2160 360 -30 1 0 117649 |
| Inv:Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A059297 | 1 0 1 0 2 1 0 3 6 1 0 4 24 12 1 0 5 80 90 20 1 0 6 240 540 240 30 1 0 7 672 2835 2240 525 42 1 0 8 |
| Inv:Rev | Accsee docs | missing | 1 1 1 1 -1 -1 1 -5 4 4 1 -11 37 -27 -27 1 -19 131 -369 256 256 1 -29 331 -1829 4651 -3125 -3125 1 |
| Inv:Rev | AccRevsee docs | missing | 1 0 1 0 -2 -1 0 9 3 4 0 -64 -16 -28 -27 0 625 125 275 255 256 0 -7776 -1296 -3456 -3096 -3126 -3125 |
| Inv:Rev | AntiDiagsee docs | missing | 1 1 1 0 1 -2 1 -6 0 1 -12 9 1 -20 48 0 1 -30 150 -64 1 -42 360 -500 0 1 -56 735 -2160 625 1 -72 |
| Inv:Rev | Diffx1T(n, k) (k+1) | missing | 1 1 0 1 -4 0 1 -12 27 0 1 -24 144 -256 0 1 -40 450 -2000 3125 0 1 -60 1080 -8640 32400 -46656 0 1 |
| Inv:Rev | RowSum∑ k=0..n T(n, k) | A000312 | 1 1 -1 4 -27 256 -3125 46656 -823543 16777216 -387420489 10000000000 -285311670611 8916100448256 |
| Inv:Rev | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 1 1 10 49 776 6841 154400 1979713 58388608 985263601 35958682112 753424361713 32805006411776 |
| Inv:Rev | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 0 -2 -6 -76 -520 -9966 -107744 -2803256 -41611392 -1372684090 -25958682112 -1038736032324 |
| Inv:Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A000272 | 1 1 3 16 125 1296 16807 262144 4782969 100000000 2357947691 61917364224 1792160394037 |
| Inv:Rev | AbsSum∑ k=0..n | T(n, k) | | A000272 | 1 1 3 16 125 1296 16807 262144 4782969 100000000 2357947691 61917364224 1792160394037 |
| Inv:Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 1 -1 -5 -2 29 57 -181 -855 893 12498 5185 -189895 -363691 2983659 11526015 -46512706 -326734419 |
| Inv:Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A000312 | 1 2 -1 4 -27 256 -3125 46656 -823543 16777216 -387420489 10000000000 -285311670611 8916100448256 |
| Inv:Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 1 -3 16 -135 1536 -21875 373248 -7411887 167772160 -4261625379 120000000000 -3709051717943 |
| Inv:Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 2 18 192 7500 38880 7058940 220200960 12053081880 63000000000 65362309994520 286058222714880 |
| Inv:Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | A000027 | 1 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:Rev | RowMaxMax k=0..n | T(n, k) | | A000169 | 1 1 2 9 64 625 7776 117649 2097152 43046721 1000000000 25937424601 743008370688 23298085122481 |
| Inv:Rev | ColMiddleT(n, n // 2) | missing | 1 1 -2 -6 48 150 -2160 -6860 143360 459270 -12600000 -40584852 1379524608 4459971516 -180889572864 |
| Inv:Rev | CentralET(2 n, n) | A367254 | 1 -2 48 -2160 143360 -12600000 1379524608 -180889572864 27638114549760 -4822114348846080 |
| Inv:Rev | CentralOT(2 n + 1, n) | missing | 1 -6 150 -6860 459270 -40584852 4459971516 -586389375000 89777998265670 -15689075866014980 |
| 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) | A367257 | 1 1 -3 10 -15 -474 12565 -258572 5136705 -102255290 2019481101 -37521627252 543274535089 |
| Inv:Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A367256 | 1 -1 5 -46 593 -9726 192637 -4457580 117769409 -3492894070 114790042901 -4137157889316 |
| Inv:Rev | TransNat0∑ k=0..n T(n, k) k | A055897 | 0 0 -2 12 -108 1280 -18750 326592 -6588344 150994944 -3874204890 110000000000 -3423740047332 |
| Inv:Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 1 -3 16 -135 1536 -21875 373248 -7411887 167772160 -4261625379 120000000000 -3709051717943 |
| Inv:Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 0 -2 30 -396 6080 -108750 2231712 -51765560 1340080128 -38311581690 1199000000000 -40773631472772 |
| Inv:Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 2 0 2 -16 162 -2048 31250 -559872 11529602 -268435456 6973568802 -200000000000 6276856753442 |
| Inv:Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A007334 | 1 -2 8 -50 432 -4802 65536 -1062882 20000000 -428717762 10319560704 -275716983698 8099130339328 |
| Inv:Rev | DiagRow1T(n + 1, n) | A000169 | 1 -2 9 -64 625 -7776 117649 -2097152 43046721 -1000000000 25937424601 -743008370688 23298085122481 |
| Inv:Rev | DiagRow2T(n + 2, n) | A053506 | 1 -6 48 -500 6480 -100842 1835008 -38263752 900000000 -23579476910 681091006464 -21505924728444 |
| Inv:Rev | DiagRow3T(n + 3, n) | A053507 | 1 -12 150 -2160 36015 -688128 14880348 -360000000 9646149645 -283787919360 9098660462034 |
| Inv:Rev | DiagCol1T(n + 1, 1) | A002378 | 0 -2 -6 -12 -20 -30 -42 -56 -72 -90 -110 -132 -156 -182 -210 -240 -272 -306 -342 -380 -420 -462 |
| Inv:Rev | DiagCol2T(n + 2, 2) | missing | 0 9 48 150 360 735 1344 2268 3600 5445 7920 11154 15288 20475 26880 34680 44064 55233 68400 83790 |
| Inv:Rev | DiagCol3T(n + 3, 3) | missing | 0 -64 -500 -2160 -6860 -17920 -40824 -84000 -159720 -285120 -483340 -784784 -1228500 -1863680 |
| Inv:Rev | Polysee docs | missing | 1 1 1 1 1 1 1 -1 1 1 1 4 -3 1 1 1 -27 25 -5 1 1 1 256 -343 64 -7 1 1 1 -3125 6561 -1331 121 -9 1 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 | 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 |
| Inv:Rev | PolyRow3∑ k=0..3 T(3, k) n^k | A016790 | 1 4 25 64 121 196 289 400 529 676 841 1024 1225 1444 1681 1936 2209 2500 2809 3136 3481 3844 4225 |
| Inv:Rev | PolyCol2∑ k=0..n T(n, k) 2^k | A085527 | 1 1 -3 25 -343 6561 -161051 4826809 -170859375 6975757441 -322687697779 16679880978201 |
| Inv:Rev | PolyCol3∑ k=0..n T(n, k) 3^k | A274265 | 1 1 -5 64 -1331 38416 -1419857 64000000 -3404825447 208827064576 -14507145975869 1125899906842624 |
| Inv:Rev | PolyDiag∑ k=0..n T(n, k) n^k | A174841 | 1 1 -3 64 -3375 331776 -52521875 12230590464 -3938980639167 1677721600000000 -913517247483640899 |
| << | 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.