OEIS Similars: A021009, A021010, A144084
| ↕ Type | ↕ Trait | ↕ Anum | ↕ Sequence |
|---|---|---|---|
| Std | TriangleT(n, k), 0 ≤ k ≤ n | A021009 | 1 1 1 2 4 1 6 18 9 1 24 96 72 16 1 120 600 600 200 25 1 720 4320 5400 2400 450 36 1 5040 35280 |
| Std | RevT(n, n - k), 0 ≤ k ≤ n | A144084 | 1 1 1 1 4 2 1 9 18 6 1 16 72 96 24 1 25 200 600 600 120 1 36 450 2400 5400 4320 720 1 49 882 7350 |
| Std | InvT-1(n, k), 0 ≤ k ≤ n | A021009 | 1 -1 1 2 -4 1 -6 18 -9 1 24 -96 72 -16 1 -120 600 -600 200 -25 1 720 -4320 5400 -2400 450 -36 1 |
| Std | RevInvT-1(n, n - k), 0 ≤ k ≤ n | A144084 | 1 1 -1 1 -4 2 1 -9 18 -6 1 -16 72 -96 24 1 -25 200 -600 600 -120 1 -36 450 -2400 5400 -4320 720 1 |
| Std | Accsee docs | missing | 1 1 2 2 6 7 6 24 33 34 24 120 192 208 209 120 720 1320 1520 1545 1546 720 5040 10440 12840 13290 |
| Std | AccRevsee docs | missing | 1 1 2 1 5 7 1 10 28 34 1 17 89 185 209 1 26 226 826 1426 1546 1 37 487 2887 8287 12607 13327 1 50 |
| Std | AntiDiagsee docs | A084950 | 1 1 2 1 6 4 24 18 1 120 96 9 720 600 72 1 5040 4320 600 16 40320 35280 5400 200 1 362880 322560 |
| Std | Diffx1T(n, k) (k+1) | missing | 1 1 2 2 8 3 6 36 27 4 24 192 216 64 5 120 1200 1800 800 125 6 720 8640 16200 9600 2250 216 7 5040 |
| Std | RowSum∑ k=0..n T(n, k) | A002720 | 1 2 7 34 209 1546 13327 130922 1441729 17572114 234662231 3405357682 53334454417 896324308634 |
| Std | EvenSum∑ k=0..n T(n, k) even(k) | A331325 | 1 1 3 15 97 745 6571 65359 723969 8842257 118091251 1712261551 26786070433 449634481465 |
| Std | OddSum∑ k=0..n T(n, k) odd(k) | A331326 | 0 1 4 19 112 801 6756 65563 717760 8729857 116570980 1693096131 26548383984 446689827169 |
| Std | AltSum∑ k=0..n T(n, k) (-1)^k | A009940 | 1 0 -1 -4 -15 -56 -185 -204 6209 112400 1520271 19165420 237686449 2944654296 36392001815 |
| Std | AbsSum∑ k=0..n | T(n, k) | | A002720 | 1 2 7 34 209 1546 13327 130922 1441729 17572114 234662231 3405357682 53334454417 896324308634 |
| Std | DiagSum∑ k=0..n // 2 T(n - k, k) | A001040 | 1 1 3 10 43 225 1393 9976 81201 740785 7489051 83120346 1004933203 13147251985 185066460993 |
| Std | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 3 15 97 753 6771 68983 783945 9820737 134352163 1991873631 31799487633 543705960625 9909847105107 |
| Std | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A000262 | 1 3 13 73 501 4051 37633 394353 4596553 58941091 824073141 12470162233 202976401213 3535017524403 |
| Std | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 4 18 288 600 21600 529200 11289600 45722880 4572288000 15367968000 2212987392000 13356959616000 |
| Std | RowGcdGcd k=0..n | T(n, k) | > 1 | A102631 | 1 1 2 3 8 5 6 7 32 27 10 11 24 13 14 15 128 17 54 19 40 21 22 23 96 125 26 243 56 29 30 31 512 33 |
| Std | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 4 18 96 600 5400 52920 564480 6531840 81648000 1097712000 17563392000 296821324800 |
| Std | ColMiddleT(n, n // 2) | A343580 | 1 1 4 18 72 600 2400 29400 117600 1905120 7620480 153679680 614718720 14841066240 59364264960 |
| Std | CentralET(2 n, n) | A295383 | 1 4 72 2400 117600 7620480 614718720 59364264960 6678479808000 857813628672000 123868287980236800 |
| Std | CentralOT(2 n + 1, n) | missing | 1 18 600 29400 1905120 153679680 14841066240 1669619952000 214453407168000 30967071995059200 |
| Std | ColLeftT(n, 0) | A000142 | 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 |
| 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) | A216831 | 1 2 11 88 905 11246 162607 2668436 48830273 983353690 21570885011 511212091952 13001401709881 |
| Std | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A343840 | 1 0 -5 22 9 -1244 14335 -79470 -586943 25131304 -434574909 4418399470 8524321465 -1771817986548 |
| Std | TransNat0∑ k=0..n T(n, k) k | A103194 | 0 1 6 39 292 2505 24306 263431 3154824 41368977 589410910 9064804551 149641946796 2638693215769 |
| Std | TransNat1∑ k=0..n T(n, k) (k + 1) | A000262 | 1 3 13 73 501 4051 37633 394353 4596553 58941091 824073141 12470162233 202976401213 3535017524403 |
| Std | TransSqrs∑ k=0..n T(n, k) k^2 | A105219 | 0 1 8 63 544 5225 55656 653023 8379008 116780049 1757211400 28394129951 490371506208 9013522796473 |
| Std | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A025167 | 1 3 17 139 1473 19091 291793 5129307 101817089 2250495523 54780588561 1455367098923 41888448785857 |
| Std | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A025166 | 1 -1 1 7 -127 1711 -23231 334391 -5144063 84149983 -1446872959 25661798119 -454494403199 |
| Std | DiagRow1T(n + 1, n) | A000290 | 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 784 |
| Std | DiagRow2T(n + 2, n) | A163102 | 2 18 72 200 450 882 1568 2592 4050 6050 8712 12168 16562 22050 28800 36992 46818 58482 72200 88200 |
| Std | DiagRow3T(n + 3, n) | A179058 | 6 96 600 2400 7350 18816 42336 86400 163350 290400 490776 794976 1242150 1881600 2774400 3995136 |
| Std | DiagCol1T(n + 1, 1) | A001563 | 1 4 18 96 600 4320 35280 322560 3265920 36288000 439084800 5748019200 80951270400 1220496076800 |
| Std | DiagCol2T(n + 2, 2) | A001809 | 1 9 72 600 5400 52920 564480 6531840 81648000 1097712000 15807052800 242853811200 3966612249600 |
| Std | DiagCol3T(n + 3, 3) | A001810 | 1 16 200 2400 29400 376320 5080320 72576000 1097712000 17563392000 296821324800 5288816332800 |
| Std | Polysee docs | A343847 | 1 1 1 2 2 1 6 7 3 1 24 34 14 4 1 120 209 86 23 5 1 720 1546 648 168 34 6 1 5040 13327 5752 1473 286 |
| 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 | A008865 | 2 7 14 23 34 47 62 79 98 119 142 167 194 223 254 287 322 359 398 439 482 527 574 623 674 727 782 |
| Std | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 6 34 86 168 286 446 654 916 1238 1626 2086 2624 3246 3958 4766 5676 6694 7826 9078 10456 11966 |
| Std | PolyCol2∑ k=0..n T(n, k) 2^k | A087912 | 1 3 14 86 648 5752 58576 671568 8546432 119401856 1815177984 29808908032 525586164736 9898343691264 |
| Std | PolyCol3∑ k=0..n T(n, k) 3^k | A277382 | 1 4 23 168 1473 14988 173007 2228544 31636449 490102164 8219695239 148262469336 2860241078817 |
| Std | PolyDiag∑ k=0..n T(n, k) n^k | A277373 | 1 2 14 168 2840 61870 1649232 51988748 1891712384 78031713690 3598075308800 183396819358192 |
| Alt | TriangleT(n, k), 0 ≤ k ≤ n | A021009 | 1 1 -1 2 -4 1 6 -18 9 -1 24 -96 72 -16 1 120 -600 600 -200 25 -1 720 -4320 5400 -2400 450 -36 1 |
| Alt | RevT(n, n - k), 0 ≤ k ≤ n | A144084 | 1 -1 1 1 -4 2 -1 9 -18 6 1 -16 72 -96 24 -1 25 -200 600 -600 120 1 -36 450 -2400 5400 -4320 720 -1 |
| Alt | InvT-1(n, k), 0 ≤ k ≤ n | missing | 1 -1 1 -6 4 1 30 -18 -9 1 792 -480 -216 16 1 -10920 6600 3000 -200 -25 1 -650160 393120 178200 |
| Alt | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 -1 1 4 -6 1 -9 -18 30 1 16 -216 -480 792 1 -25 -200 3000 6600 -10920 1 36 -1350 -12000 178200 |
| Alt | Accsee docs | missing | 1 1 0 2 -2 -1 6 -12 -3 -4 24 -72 0 -16 -15 120 -480 120 -80 -55 -56 720 -3600 1800 -600 -150 -186 |
| Alt | AccRevsee docs | missing | 1 -1 0 1 -3 -1 -1 8 -10 -4 1 -15 57 -39 -15 -1 24 -176 424 -176 -56 1 -35 415 -1985 3415 -905 -185 |
| Alt | AntiDiagsee docs | A084950 | 1 1 2 -1 6 -4 24 -18 1 120 -96 9 720 -600 72 -1 5040 -4320 600 -16 40320 -35280 5400 -200 1 362880 |
| Alt | Diffx1T(n, k) (k+1) | missing | 1 1 -2 2 -8 3 6 -36 27 -4 24 -192 216 -64 5 120 -1200 1800 -800 125 -6 720 -8640 16200 -9600 2250 |
| Alt | RowSum∑ k=0..n T(n, k) | A009940 | 1 0 -1 -4 -15 -56 -185 -204 6209 112400 1520271 19165420 237686449 2944654296 36392001815 |
| Alt | EvenSum∑ k=0..n T(n, k) even(k) | A331325 | 1 1 3 15 97 745 6571 65359 723969 8842257 118091251 1712261551 26786070433 449634481465 |
| Alt | OddSum∑ k=0..n T(n, k) odd(k) | A331326 | 0 -1 -4 -19 -112 -801 -6756 -65563 -717760 -8729857 -116570980 -1693096131 -26548383984 |
| Alt | AltSum∑ k=0..n T(n, k) (-1)^k | A002720 | 1 2 7 34 209 1546 13327 130922 1441729 17572114 234662231 3405357682 53334454417 896324308634 |
| Alt | AbsSum∑ k=0..n | T(n, k) | | A002720 | 1 2 7 34 209 1546 13327 130922 1441729 17572114 234662231 3405357682 53334454417 896324308634 |
| Alt | DiagSum∑ k=0..n // 2 T(n - k, k) | A058797 | 1 1 1 2 7 33 191 1304 10241 90865 898409 9791634 116601199 1506023953 20967734143 313009988192 |
| Alt | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 1 -1 -13 -79 -431 -2201 -9269 -6847 615329 12760271 203118211 2997506929 43113664177 613544243831 |
| Alt | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 -1 -3 -7 -11 39 721 7433 68937 621071 5482981 46032249 330103357 1056150263 -31272214791 |
| Alt | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 4 18 288 600 21600 529200 11289600 45722880 4572288000 15367968000 2212987392000 13356959616000 |
| Alt | RowGcdGcd k=0..n | T(n, k) | > 1 | A102631 | 1 1 2 3 8 5 6 7 32 27 10 11 24 13 14 15 128 17 54 19 40 21 22 23 96 125 26 243 56 29 30 31 512 33 |
| Alt | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 4 18 96 600 5400 52920 564480 6531840 81648000 1097712000 17563392000 296821324800 |
| Alt | ColMiddleT(n, n // 2) | A343580 | 1 1 -4 -18 72 600 -2400 -29400 117600 1905120 -7620480 -153679680 614718720 14841066240 |
| Alt | CentralET(2 n, n) | A295383 | 1 -4 72 -2400 117600 -7620480 614718720 -59364264960 6678479808000 -857813628672000 |
| Alt | CentralOT(2 n + 1, n) | missing | 1 -18 600 -29400 1905120 -153679680 14841066240 -1669619952000 214453407168000 -30967071995059200 |
| Alt | ColLeftT(n, 0) | A000142 | 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 |
| Alt | BinConv∑ k=0..n C(n, k) T(n, k) | A343840 | 1 0 -5 -22 9 1244 14335 79470 -586943 -25131304 -434574909 -4418399470 8524321465 1771817986548 |
| Alt | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A216831 | 1 -2 11 -88 905 -11246 162607 -2668436 48830273 -983353690 21570885011 -511212091952 13001401709881 |
| Alt | TransNat0∑ k=0..n T(n, k) k | missing | 0 -1 -2 -3 4 95 906 7637 62728 508671 3962710 26866829 92416908 -1888504033 -67664216606 |
| Alt | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 -1 -3 -7 -11 39 721 7433 68937 621071 5482981 46032249 330103357 1056150263 -31272214791 |
| Alt | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 -1 0 9 64 375 2016 9065 13056 -502929 -11240000 -183952791 -2759820480 -40169009881 -577152242016 |
| Alt | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A025166 | 1 1 1 -7 -127 -1711 -23231 -334391 -5144063 -84149983 -1446872959 -25661798119 -454494403199 |
| Alt | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A025167 | 1 -3 17 -139 1473 -19091 291793 -5129307 101817089 -2250495523 54780588561 -1455367098923 |
| Alt | DiagRow1T(n + 1, n) | A000290 | 1 -4 9 -16 25 -36 49 -64 81 -100 121 -144 169 -196 225 -256 289 -324 361 -400 441 -484 529 -576 625 |
| Alt | DiagRow2T(n + 2, n) | A163102 | 2 -18 72 -200 450 -882 1568 -2592 4050 -6050 8712 -12168 16562 -22050 28800 -36992 46818 -58482 |
| Alt | DiagRow3T(n + 3, n) | A179058 | 6 -96 600 -2400 7350 -18816 42336 -86400 163350 -290400 490776 -794976 1242150 -1881600 2774400 |
| Alt | DiagCol1T(n + 1, 1) | A001563 | -1 -4 -18 -96 -600 -4320 -35280 -322560 -3265920 -36288000 -439084800 -5748019200 -80951270400 |
| Alt | DiagCol2T(n + 2, 2) | A001809 | 1 9 72 600 5400 52920 564480 6531840 81648000 1097712000 15807052800 242853811200 3966612249600 |
| Alt | DiagCol3T(n + 3, 3) | A001810 | -1 -16 -200 -2400 -29400 -376320 -5080320 -72576000 -1097712000 -17563392000 -296821324800 |
| Alt | Polysee docs | missing | 1 1 1 2 0 1 6 -1 -1 1 24 -4 -2 -2 1 120 -15 -2 -1 -3 1 720 -56 8 6 2 -4 1 5040 -185 88 33 14 7 -5 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 | A008865 | 2 -1 -2 -1 2 7 14 23 34 47 62 79 98 119 142 167 194 223 254 287 322 359 398 439 482 527 574 623 674 |
| Alt | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 6 -4 -2 6 14 16 6 -22 -74 -156 -274 -434 -642 -904 -1226 -1614 -2074 -2612 -3234 -3946 -4754 -5664 |
| Alt | PolyCol2∑ k=0..n T(n, k) 2^k | A295382 | 1 -1 -2 -2 8 88 592 3344 14464 2944 -1121536 -21603584 -317969408 -4202380288 -51322677248 |
| Alt | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 -2 -1 6 33 102 -9 -3762 -44703 -385074 -2540241 -7216938 163030401 4625907894 83469651687 |
| Alt | PolyDiag∑ k=0..n T(n, k) n^k | A277423 | 1 0 -2 6 24 -380 720 31794 -361088 -2104056 101548800 -612792290 -25534891008 593660731404 |
| Rev | TriangleT(n, k), 0 ≤ k ≤ n | A144084 | 1 1 1 1 4 2 1 9 18 6 1 16 72 96 24 1 25 200 600 600 120 1 36 450 2400 5400 4320 720 1 49 882 7350 |
| Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A021009 | 1 -1 1 2 -4 1 -6 18 -9 1 24 -96 72 -16 1 -120 600 -600 200 -25 1 720 -4320 5400 -2400 450 -36 1 |
| Rev | Accsee docs | missing | 1 1 2 1 5 7 1 10 28 34 1 17 89 185 209 1 26 226 826 1426 1546 1 37 487 2887 8287 12607 13327 1 50 |
| Rev | AccRevsee docs | missing | 1 1 2 2 6 7 6 24 33 34 24 120 192 208 209 120 720 1320 1520 1545 1546 720 5040 10440 12840 13290 |
| Rev | AntiDiagsee docs | missing | 1 1 1 1 1 4 1 9 2 1 16 18 1 25 72 6 1 36 200 96 1 49 450 600 24 1 64 882 2400 600 1 81 1568 7350 |
| Rev | Diffx1T(n, k) (k+1) | missing | 1 1 2 1 8 6 1 18 54 24 1 32 216 384 120 1 50 600 2400 3000 720 1 72 1350 9600 27000 25920 5040 1 98 |
| Rev | RowSum∑ k=0..n T(n, k) | A002720 | 1 2 7 34 209 1546 13327 130922 1441729 17572114 234662231 3405357682 53334454417 896324308634 |
| Rev | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 1 3 19 97 801 6571 65563 723969 8729857 118091251 1693096131 26786070433 446689827169 |
| Rev | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 1 4 15 112 745 6756 65359 717760 8842257 116570980 1712261551 26548383984 449634481465 |
| Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A009940 | 1 0 -1 4 -15 56 -185 204 6209 -112400 1520271 -19165420 237686449 -2944654296 36392001815 |
| Rev | AbsSum∑ k=0..n | T(n, k) | | A002720 | 1 2 7 34 209 1546 13327 130922 1441729 17572114 234662231 3405357682 53334454417 896324308634 |
| Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 2 5 12 35 104 333 1124 3947 14520 55229 217748 885219 3705272 15939725 70325604 317879963 |
| Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A000262 | 1 3 13 73 501 4051 37633 394353 4596553 58941091 824073141 12470162233 202976401213 3535017524403 |
| Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 3 15 97 753 6771 68983 783945 9820737 134352163 1991873631 31799487633 543705960625 9909847105107 |
| Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 4 18 288 600 21600 529200 11289600 45722880 4572288000 15367968000 2212987392000 13356959616000 |
| Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | A102631 | 1 1 2 3 8 5 6 7 32 27 10 11 24 13 14 15 128 17 54 19 40 21 22 23 96 125 26 243 56 29 30 31 512 33 |
| Rev | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 4 18 96 600 5400 52920 564480 6531840 81648000 1097712000 17563392000 296821324800 |
| Rev | ColMiddleT(n, n // 2) | missing | 1 1 4 9 72 200 2400 7350 117600 381024 7620480 25613280 614718720 2120152320 59364264960 |
| Rev | CentralET(2 n, n) | A295383 | 1 4 72 2400 117600 7620480 614718720 59364264960 6678479808000 857813628672000 123868287980236800 |
| Rev | CentralOT(2 n + 1, n) | missing | 1 9 200 7350 381024 25613280 2120152320 208702494000 23828156352000 3096707199505920 |
| 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) | A000142 | 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 |
| Rev | BinConv∑ k=0..n C(n, k) T(n, k) | A216831 | 1 2 11 88 905 11246 162607 2668436 48830273 983353690 21570885011 511212091952 13001401709881 |
| Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A343840 | 1 0 -5 -22 9 1244 14335 79470 -586943 -25131304 -434574909 -4418399470 8524321465 1771817986548 |
| Rev | TransNat0∑ k=0..n T(n, k) k | A105219 | 0 1 8 63 544 5225 55656 653023 8379008 116780049 1757211400 28394129951 490371506208 9013522796473 |
| Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 3 15 97 753 6771 68983 783945 9820737 134352163 1991873631 31799487633 543705960625 9909847105107 |
| Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 12 135 1552 18825 243756 3380167 50172480 795479697 13435216300 241016709351 4579126219152 |
| Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A087912 | 1 3 14 86 648 5752 58576 671568 8546432 119401856 1815177984 29808908032 525586164736 9898343691264 |
| Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A295382 | 1 -1 -2 -2 8 88 592 3344 14464 2944 -1121536 -21603584 -317969408 -4202380288 -51322677248 |
| Rev | DiagRow1T(n + 1, n) | A001563 | 1 4 18 96 600 4320 35280 322560 3265920 36288000 439084800 5748019200 80951270400 1220496076800 |
| Rev | DiagRow2T(n + 2, n) | A001809 | 1 9 72 600 5400 52920 564480 6531840 81648000 1097712000 15807052800 242853811200 3966612249600 |
| Rev | DiagRow3T(n + 3, n) | A001810 | 1 16 200 2400 29400 376320 5080320 72576000 1097712000 17563392000 296821324800 5288816332800 |
| Rev | DiagCol1T(n + 1, 1) | A000290 | 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 784 |
| Rev | DiagCol2T(n + 2, 2) | A163102 | 2 18 72 200 450 882 1568 2592 4050 6050 8712 12168 16562 22050 28800 36992 46818 58482 72200 88200 |
| Rev | DiagCol3T(n + 3, 3) | A179058 | 6 96 600 2400 7350 18816 42336 86400 163350 290400 490776 794976 1242150 1881600 2774400 3995136 |
| Rev | Polysee docs | missing | 1 1 1 1 2 1 1 7 3 1 1 34 17 4 1 1 209 139 31 5 1 1 1546 1473 352 49 6 1 1 13327 19091 5233 709 71 7 |
| 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 | A056220 | 1 7 17 31 49 71 97 127 161 199 241 287 337 391 449 511 577 647 721 799 881 967 1057 1151 1249 1351 |
| Rev | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 1 34 139 352 709 1246 1999 3004 4297 5914 7891 10264 13069 16342 20119 24436 29329 34834 40987 |
| Rev | PolyCol2∑ k=0..n T(n, k) 2^k | A025167 | 1 3 17 139 1473 19091 291793 5129307 101817089 2250495523 54780588561 1455367098923 41888448785857 |
| Rev | PolyCol3∑ k=0..n T(n, k) 3^k | A102757 | 1 4 31 352 5233 95836 2080999 52189096 1482977857 47053929268 1648037039791 63125834205424 |
| Rev | PolyDiag∑ k=0..n T(n, k) n^k | A330260 | 1 2 17 352 13505 830126 74717857 9263893892 1513712421377 315230799073690 81499084718806001 |
| Inv | TriangleT(n, k), 0 ≤ k ≤ n | A021009 | 1 -1 1 2 -4 1 -6 18 -9 1 24 -96 72 -16 1 -120 600 -600 200 -25 1 720 -4320 5400 -2400 450 -36 1 |
| Inv | RevT(n, n - k), 0 ≤ k ≤ n | A144084 | 1 1 -1 1 -4 2 1 -9 18 -6 1 -16 72 -96 24 1 -25 200 -600 600 -120 1 -36 450 -2400 5400 -4320 720 1 |
| Inv | RevInvT-1(n, n - k), 0 ≤ k ≤ n | A144084 | 1 1 1 1 4 2 1 9 18 6 1 16 72 96 24 1 25 200 600 600 120 1 36 450 2400 5400 4320 720 1 49 882 7350 |
| Inv | Accsee docs | missing | 1 -1 0 2 -2 -1 -6 12 3 4 24 -72 0 -16 -15 -120 480 -120 80 55 56 720 -3600 1800 -600 -150 -186 -185 |
| Inv | AccRevsee docs | missing | 1 1 0 1 -3 -1 1 -8 10 4 1 -15 57 -39 -15 1 -24 176 -424 176 56 1 -35 415 -1985 3415 -905 -185 1 -48 |
| Inv | AntiDiagsee docs | A084950 | 1 -1 2 1 -6 -4 24 18 1 -120 -96 -9 720 600 72 1 -5040 -4320 -600 -16 40320 35280 5400 200 1 -362880 |
| Inv | Diffx1T(n, k) (k+1) | missing | 1 -1 2 2 -8 3 -6 36 -27 4 24 -192 216 -64 5 -120 1200 -1800 800 -125 6 720 -8640 16200 -9600 2250 |
| Inv | RowSum∑ k=0..n T(n, k) | A009940 | 1 0 -1 4 -15 56 -185 204 6209 -112400 1520271 -19165420 237686449 -2944654296 36392001815 |
| Inv | EvenSum∑ k=0..n T(n, k) even(k) | A331325 | 1 -1 3 -15 97 -745 6571 -65359 723969 -8842257 118091251 -1712261551 26786070433 -449634481465 |
| Inv | OddSum∑ k=0..n T(n, k) odd(k) | A331326 | 0 1 -4 19 -112 801 -6756 65563 -717760 8729857 -116570980 1693096131 -26548383984 446689827169 |
| Inv | AltSum∑ k=0..n T(n, k) (-1)^k | A002720 | 1 -2 7 -34 209 -1546 13327 -130922 1441729 -17572114 234662231 -3405357682 53334454417 |
| Inv | AbsSum∑ k=0..n | T(n, k) | | A002720 | 1 2 7 34 209 1546 13327 130922 1441729 17572114 234662231 3405357682 53334454417 896324308634 |
| Inv | DiagSum∑ k=0..n // 2 T(n - k, k) | A001040 | 1 -1 3 -10 43 -225 1393 -9976 81201 -740785 7489051 -83120346 1004933203 -13147251985 185066460993 |
| Inv | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 -1 -1 13 -79 431 -2201 9269 -6847 -615329 12760271 -203118211 2997506929 -43113664177 |
| Inv | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 1 -3 7 -11 -39 721 -7433 68937 -621071 5482981 -46032249 330103357 -1056150263 -31272214791 |
| Inv | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 4 18 288 600 21600 529200 11289600 45722880 4572288000 15367968000 2212987392000 13356959616000 |
| Inv | RowGcdGcd k=0..n | T(n, k) | > 1 | A102631 | 1 1 2 3 8 5 6 7 32 27 10 11 24 13 14 15 128 17 54 19 40 21 22 23 96 125 26 243 56 29 30 31 512 33 |
| Inv | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 4 18 96 600 5400 52920 564480 6531840 81648000 1097712000 17563392000 296821324800 |
| Inv | ColMiddleT(n, n // 2) | A343580 | 1 -1 -4 18 72 -600 -2400 29400 117600 -1905120 -7620480 153679680 614718720 -14841066240 |
| Inv | CentralET(2 n, n) | A295383 | 1 -4 72 -2400 117600 -7620480 614718720 -59364264960 6678479808000 -857813628672000 |
| Inv | CentralOT(2 n + 1, n) | missing | -1 18 -600 29400 -1905120 153679680 -14841066240 1669619952000 -214453407168000 30967071995059200 |
| Inv | ColLeftT(n, 0) | A000142 | 1 -1 2 -6 24 -120 720 -5040 40320 -362880 3628800 -39916800 479001600 -6227020800 87178291200 |
| 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) | A343840 | 1 0 -5 22 9 -1244 14335 -79470 -586943 25131304 -434574909 4418399470 8524321465 -1771817986548 |
| Inv | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A216831 | 1 2 11 88 905 11246 162607 2668436 48830273 983353690 21570885011 511212091952 13001401709881 |
| Inv | TransNat0∑ k=0..n T(n, k) k | missing | 0 1 -2 3 4 -95 906 -7637 62728 -508671 3962710 -26866829 92416908 1888504033 -67664216606 |
| Inv | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 1 -3 7 -11 -39 721 -7433 68937 -621071 5482981 -46032249 330103357 -1056150263 -31272214791 |
| Inv | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 0 -9 64 -375 2016 -9065 13056 502929 -11240000 183952791 -2759820480 40169009881 -577152242016 |
| Inv | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A025166 | 1 -1 1 7 -127 1711 -23231 334391 -5144063 84149983 -1446872959 25661798119 -454494403199 |
| Inv | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A025167 | 1 3 17 139 1473 19091 291793 5129307 101817089 2250495523 54780588561 1455367098923 41888448785857 |
| Inv | DiagRow1T(n + 1, n) | A000290 | -1 -4 -9 -16 -25 -36 -49 -64 -81 -100 -121 -144 -169 -196 -225 -256 -289 -324 -361 -400 -441 -484 |
| Inv | DiagRow2T(n + 2, n) | A163102 | 2 18 72 200 450 882 1568 2592 4050 6050 8712 12168 16562 22050 28800 36992 46818 58482 72200 88200 |
| Inv | DiagRow3T(n + 3, n) | A179058 | -6 -96 -600 -2400 -7350 -18816 -42336 -86400 -163350 -290400 -490776 -794976 -1242150 -1881600 |
| Inv | DiagCol1T(n + 1, 1) | A001563 | 1 -4 18 -96 600 -4320 35280 -322560 3265920 -36288000 439084800 -5748019200 80951270400 |
| Inv | DiagCol2T(n + 2, 2) | A001809 | 1 -9 72 -600 5400 -52920 564480 -6531840 81648000 -1097712000 15807052800 -242853811200 |
| Inv | DiagCol3T(n + 3, 3) | A001810 | 1 -16 200 -2400 29400 -376320 5080320 -72576000 1097712000 -17563392000 296821324800 -5288816332800 |
| Inv | Polysee docs | missing | 1 -1 1 2 0 1 -6 -1 1 1 24 4 -2 2 1 -120 -15 2 -1 3 1 720 56 8 -6 2 4 1 -5040 -185 -88 33 -14 7 5 1 |
| Inv | PolyRow1∑ k=0..1 T(1, k) n^k | A000027 | -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 |
| Inv | PolyRow2∑ k=0..2 T(2, k) n^k | A008865 | 2 -1 -2 -1 2 7 14 23 34 47 62 79 98 119 142 167 194 223 254 287 322 359 398 439 482 527 574 623 674 |
| Inv | PolyRow3∑ k=0..3 T(3, k) n^k | missing | -6 4 2 -6 -14 -16 -6 22 74 156 274 434 642 904 1226 1614 2074 2612 3234 3946 4754 5664 6682 7814 |
| Inv | PolyCol2∑ k=0..n T(n, k) 2^k | A295382 | 1 1 -2 2 8 -88 592 -3344 14464 -2944 -1121536 21603584 -317969408 4202380288 -51322677248 |
| Inv | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 2 -1 -6 33 -102 -9 3762 -44703 385074 -2540241 7216938 163030401 -4625907894 83469651687 |
| Inv | PolyDiag∑ k=0..n T(n, k) n^k | A277423 | 1 0 -2 -6 24 380 720 -31794 -361088 2104056 101548800 612792290 -25534891008 -593660731404 |
| Inv:Rev | TriangleT(n, k), 0 ≤ k ≤ n | A144084 | 1 1 -1 1 -4 2 1 -9 18 -6 1 -16 72 -96 24 1 -25 200 -600 600 -120 1 -36 450 -2400 5400 -4320 720 1 |
| Inv:Rev | RevT(n, n - k), 0 ≤ k ≤ n | A021009 | 1 -1 1 2 -4 1 -6 18 -9 1 24 -96 72 -16 1 -120 600 -600 200 -25 1 720 -4320 5400 -2400 450 -36 1 |
| Inv:Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A021009 | 1 1 1 2 4 1 6 18 9 1 24 96 72 16 1 120 600 600 200 25 1 720 4320 5400 2400 450 36 1 5040 35280 |
| Inv:Rev | Accsee docs | missing | 1 1 0 1 -3 -1 1 -8 10 4 1 -15 57 -39 -15 1 -24 176 -424 176 56 1 -35 415 -1985 3415 -905 -185 1 -48 |
| Inv:Rev | AccRevsee docs | missing | 1 -1 0 2 -2 -1 -6 12 3 4 24 -72 0 -16 -15 -120 480 -120 80 55 56 720 -3600 1800 -600 -150 -186 -185 |
| Inv:Rev | AntiDiagsee docs | missing | 1 1 1 -1 1 -4 1 -9 2 1 -16 18 1 -25 72 -6 1 -36 200 -96 1 -49 450 -600 24 1 -64 882 -2400 600 1 -81 |
| Inv:Rev | Diffx1T(n, k) (k+1) | missing | 1 1 -2 1 -8 6 1 -18 54 -24 1 -32 216 -384 120 1 -50 600 -2400 3000 -720 1 -72 1350 -9600 27000 |
| Inv:Rev | RowSum∑ k=0..n T(n, k) | A009940 | 1 0 -1 4 -15 56 -185 204 6209 -112400 1520271 -19165420 237686449 -2944654296 36392001815 |
| Inv:Rev | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 1 3 19 97 801 6571 65563 723969 8729857 118091251 1693096131 26786070433 446689827169 |
| Inv:Rev | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 -1 -4 -15 -112 -745 -6756 -65359 -717760 -8842257 -116570980 -1712261551 -26548383984 |
| Inv:Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A002720 | 1 2 7 34 209 1546 13327 130922 1441729 17572114 234662231 3405357682 53334454417 896324308634 |
| Inv:Rev | AbsSum∑ k=0..n | T(n, k) | | A002720 | 1 2 7 34 209 1546 13327 130922 1441729 17572114 234662231 3405357682 53334454417 896324308634 |
| Inv:Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 0 -3 -6 3 42 69 -174 -981 -582 8757 26994 -40509 -442086 -527547 5053362 20594139 -28782054 |
| Inv:Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 1 -3 7 -11 -39 721 -7433 68937 -621071 5482981 -46032249 330103357 -1056150263 -31272214791 |
| Inv:Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 -1 -1 13 -79 431 -2201 9269 -6847 -615329 12760271 -203118211 2997506929 -43113664177 |
| Inv:Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 4 18 288 600 21600 529200 11289600 45722880 4572288000 15367968000 2212987392000 13356959616000 |
| Inv:Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | A102631 | 1 1 2 3 8 5 6 7 32 27 10 11 24 13 14 15 128 17 54 19 40 21 22 23 96 125 26 243 56 29 30 31 512 33 |
| Inv:Rev | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 4 18 96 600 5400 52920 564480 6531840 81648000 1097712000 17563392000 296821324800 |
| Inv:Rev | ColMiddleT(n, n // 2) | missing | 1 1 -4 -9 72 200 -2400 -7350 117600 381024 -7620480 -25613280 614718720 2120152320 -59364264960 |
| Inv:Rev | CentralET(2 n, n) | A295383 | 1 -4 72 -2400 117600 -7620480 614718720 -59364264960 6678479808000 -857813628672000 |
| Inv:Rev | CentralOT(2 n + 1, n) | missing | 1 -9 200 -7350 381024 -25613280 2120152320 -208702494000 23828156352000 -3096707199505920 |
| 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) | A000142 | 1 -1 2 -6 24 -120 720 -5040 40320 -362880 3628800 -39916800 479001600 -6227020800 87178291200 |
| Inv:Rev | BinConv∑ k=0..n C(n, k) T(n, k) | A343840 | 1 0 -5 22 9 -1244 14335 -79470 -586943 25131304 -434574909 4418399470 8524321465 -1771817986548 |
| Inv:Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A216831 | 1 -2 11 -88 905 -11246 162607 -2668436 48830273 -983353690 21570885011 -511212091952 13001401709881 |
| Inv:Rev | TransNat0∑ k=0..n T(n, k) k | missing | 0 -1 0 9 -64 375 -2016 9065 -13056 -502929 11240000 -183952791 2759820480 -40169009881 577152242016 |
| Inv:Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 -1 -1 13 -79 431 -2201 9269 -6847 -615329 12760271 -203118211 2997506929 -43113664177 |
| Inv:Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 -1 4 9 -208 1975 -15516 107849 -593216 554607 61532900 -1543992791 29249022384 -506578671001 |
| Inv:Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A295382 | 1 1 -2 2 8 -88 592 -3344 14464 -2944 -1121536 21603584 -317969408 4202380288 -51322677248 |
| Inv:Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A087912 | 1 -3 14 -86 648 -5752 58576 -671568 8546432 -119401856 1815177984 -29808908032 525586164736 |
| Inv:Rev | DiagRow1T(n + 1, n) | A001563 | 1 -4 18 -96 600 -4320 35280 -322560 3265920 -36288000 439084800 -5748019200 80951270400 |
| Inv:Rev | DiagRow2T(n + 2, n) | A001809 | 1 -9 72 -600 5400 -52920 564480 -6531840 81648000 -1097712000 15807052800 -242853811200 |
| Inv:Rev | DiagRow3T(n + 3, n) | A001810 | 1 -16 200 -2400 29400 -376320 5080320 -72576000 1097712000 -17563392000 296821324800 -5288816332800 |
| Inv:Rev | DiagCol1T(n + 1, 1) | A000290 | -1 -4 -9 -16 -25 -36 -49 -64 -81 -100 -121 -144 -169 -196 -225 -256 -289 -324 -361 -400 -441 -484 |
| Inv:Rev | DiagCol2T(n + 2, 2) | A163102 | 2 18 72 200 450 882 1568 2592 4050 6050 8712 12168 16562 22050 28800 36992 46818 58482 72200 88200 |
| Inv:Rev | DiagCol3T(n + 3, 3) | A179058 | -6 -96 -600 -2400 -7350 -18816 -42336 -86400 -163350 -290400 -490776 -794976 -1242150 -1881600 |
| Inv:Rev | Polysee docs | missing | 1 1 1 1 0 1 1 -1 -1 1 1 4 1 -2 1 1 -15 7 7 -3 1 1 56 -127 -26 17 -4 1 1 -185 1711 -47 -131 31 -5 1 |
| Inv:Rev | PolyRow1∑ k=0..1 T(1, k) n^k | A000027 | 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 -13 -14 -15 -16 -17 -18 -19 -20 -21 -22 -23 -24 -25 -26 |
| Inv:Rev | PolyRow2∑ k=0..2 T(2, k) n^k | A056220 | 1 -1 1 7 17 31 49 71 97 127 161 199 241 287 337 391 449 511 577 647 721 799 881 967 1057 1151 1249 |
| Inv:Rev | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 1 4 7 -26 -131 -344 -701 -1238 -1991 -2996 -4289 -5906 -7883 -10256 -13061 -16334 -20111 -24428 |
| Inv:Rev | PolyCol2∑ k=0..n T(n, k) 2^k | A025166 | 1 -1 1 7 -127 1711 -23231 334391 -5144063 84149983 -1446872959 25661798119 -454494403199 |
| Inv:Rev | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 -2 7 -26 -47 4966 -148337 4027822 -111807551 3270352078 -101632011689 3357867854518 |
| Inv:Rev | PolyDiag∑ k=0..n T(n, k) n^k | A330497 | 1 0 1 -26 1089 -70124 6495985 -821315214 136115947009 -28651724077976 7470040450004001 |
| << | 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.