OEIS Similars: A271703, A008297, A066667, A089231, A105278, A111596
| ↕ Type | ↕ Trait | ↕ Anum | ↕ Sequence |
|---|---|---|---|
| Std | TriangleT(n, k), 0 ≤ k ≤ n | A271703 | 1 0 1 0 2 1 0 6 6 1 0 24 36 12 1 0 120 240 120 20 1 0 720 1800 1200 300 30 1 0 5040 15120 12600 |
| Std | RevT(n, n - k), 0 ≤ k ≤ n | missing | 1 1 0 1 2 0 1 6 6 0 1 12 36 24 0 1 20 120 240 120 0 1 30 300 1200 1800 720 0 1 42 630 4200 12600 |
| Std | InvT-1(n, k), 0 ≤ k ≤ n | A271703 | 1 0 1 0 -2 1 0 6 -6 1 0 -24 36 -12 1 0 120 -240 120 -20 1 0 -720 1800 -1200 300 -30 1 0 5040 -15120 |
| Std | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 0 1 -2 0 1 -6 6 0 1 -12 36 -24 0 1 -20 120 -240 120 0 1 -30 300 -1200 1800 -720 0 1 -42 630 |
| Std | Accsee docs | A349776 | 1 0 1 0 2 3 0 6 12 13 0 24 60 72 73 0 120 360 480 500 501 0 720 2520 3720 4020 4050 4051 0 5040 |
| Std | AccRevsee docs | missing | 1 1 1 1 3 3 1 7 13 13 1 13 49 73 73 1 21 141 381 501 501 1 31 331 1531 3331 4051 4051 1 43 673 4873 |
| Std | AntiDiagsee docs | A180047 | 1 0 0 1 0 2 0 6 1 0 24 6 0 120 36 1 0 720 240 12 0 5040 1800 120 1 0 40320 15120 1200 20 0 362880 |
| Std | Diffx1T(n, k) (k+1) | A360205 | 1 0 2 0 4 3 0 12 18 4 0 48 108 48 5 0 240 720 480 100 6 0 1440 5400 4800 1500 180 7 0 10080 45360 |
| Std | RowSum∑ k=0..n T(n, k) | A000262 | 1 1 3 13 73 501 4051 37633 394353 4596553 58941091 824073141 12470162233 202976401213 3535017524403 |
| Std | EvenSum∑ k=0..n T(n, k) even(k) | A088312 | 1 0 1 6 37 260 2101 19362 201097 2326536 29668681 413257790 6238931821 101415565836 1765092183037 |
| Std | OddSum∑ k=0..n T(n, k) odd(k) | A088313 | 0 1 2 7 36 241 1950 18271 193256 2270017 29272410 410815351 6231230412 101560835377 1769925341366 |
| Std | AltSum∑ k=0..n T(n, k) (-1)^k | A111884 | 1 -1 -1 -1 1 19 151 1091 7841 56519 396271 2442439 7701409 -145269541 -4833158329 -104056218421 |
| Std | AbsSum∑ k=0..n | T(n, k) | | A000262 | 1 1 3 13 73 501 4051 37633 394353 4596553 58941091 824073141 12470162233 202976401213 3535017524403 |
| Std | DiagSum∑ k=0..n // 2 T(n - k, k) | A001053 | 1 0 1 2 7 30 157 972 6961 56660 516901 5225670 57999271 701216922 9173819257 129134686520 |
| Std | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A062147 | 1 1 5 31 229 1961 19081 207775 2501801 32989969 472630861 7307593151 121247816845 2148321709561 |
| Std | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A002720 | 1 2 7 34 209 1546 13327 130922 1441729 17572114 234662231 3405357682 53334454417 896324308634 |
| Std | RowLcmLcm k=0..n | T(n, k) | > 1 | A359365 | 1 1 2 6 72 240 3600 75600 1411200 10160640 457228800 4191264000 184415616000 2054916864000 |
| Std | RowGcdGcd k=0..n | T(n, k) | > 1 | A002378 | 1 1 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 |
| Std | RowMaxMax k=0..n | T(n, k) | | A002868 | 1 1 2 6 36 240 1800 15120 141120 1693440 21772800 299376000 4390848000 68497228800 1133317785600 |
| Std | ColMiddleT(n, n // 2) | A343581 | 1 0 2 6 36 240 1200 12600 58800 846720 3810240 69854400 307359360 6849722880 29682132480 |
| Std | CentralET(2 n, n) | A187535 | 1 2 36 1200 58800 3810240 307359360 29682132480 3339239904000 428906814336000 61934143990118400 |
| Std | CentralOT(2 n + 1, n) | A367776 | 0 6 240 12600 846720 69854400 6849722880 779155977600 100919250432000 14668613050291200 |
| 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) | A344051 | 1 1 5 37 361 4301 60001 954325 16984577 333572041 7151967181 165971975621 4139744524345 |
| Std | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A344050 | 1 1 -3 1 73 -699 3001 24697 -783999 10946233 -80958779 -656003919 40097528857 -944102982419 |
| Std | TransNat0∑ k=0..n T(n, k) k | A052852 | 0 1 4 21 136 1045 9276 93289 1047376 12975561 175721140 2581284541 40864292184 693347907421 |
| Std | TransNat1∑ k=0..n T(n, k) (k + 1) | A002720 | 1 2 7 34 209 1546 13327 130922 1441729 17572114 234662231 3405357682 53334454417 896324308634 |
| Std | TransSqrs∑ k=0..n T(n, k) k^2 | A103194 | 0 1 6 39 292 2505 24306 263431 3154824 41368977 589410910 9064804551 149641946796 2638693215769 |
| Std | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A025168 | 1 1 5 37 361 4361 62701 1044205 19748177 417787921 9770678101 250194150581 6959638411705 |
| Std | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A318223 | 1 1 -3 13 -71 441 -2699 9157 206193 -8443151 236126701 -6169406979 161388751657 -4327824442967 |
| 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) | A083374 | 0 6 36 120 300 630 1176 2016 3240 4950 7260 10296 14196 19110 25200 32640 41616 52326 64980 79800 |
| Std | DiagRow3T(n + 3, n) | A253285 | 0 24 240 1200 4200 11760 28224 60480 118800 217800 377520 624624 993720 1528800 2284800 3329280 |
| Std | DiagCol1T(n + 1, 1) | A000142 | 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 1307674368000 |
| Std | DiagCol2T(n + 2, 2) | A001286 | 1 6 36 240 1800 15120 141120 1451520 16329600 199584000 2634508800 37362124800 566658892800 |
| Std | DiagCol3T(n + 3, 3) | A001754 | 1 12 120 1200 12600 141120 1693440 21772800 299376000 4390848000 68497228800 1133317785600 |
| Std | Polysee docs | A253286 | 1 0 1 0 1 1 0 3 2 1 0 13 8 3 1 0 73 44 15 4 1 0 501 304 99 24 5 1 0 4051 2512 801 184 35 6 1 0 |
| 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 | A226514 | 0 13 44 99 184 305 468 679 944 1269 1660 2123 2664 3289 4004 4815 5728 6749 7884 9139 10520 12033 |
| Std | PolyCol2∑ k=0..n T(n, k) 2^k | A052897 | 1 2 8 44 304 2512 24064 261536 3173888 42483968 621159424 9841950208 167879268352 3065723549696 |
| Std | PolyCol3∑ k=0..n T(n, k) 3^k | A255806 | 1 3 15 99 801 7623 83079 1017495 13808097 205374123 3318673599 57845821707 1081091446785 |
| Std | PolyDiag∑ k=0..n T(n, k) n^k | A293145 | 1 1 8 99 1696 37225 997056 31535371 1150303232 47538819729 2195314048000 112032721984051 |
| Alt | TriangleT(n, k), 0 ≤ k ≤ n | A271703 | 1 0 -1 0 -2 1 0 -6 6 -1 0 -24 36 -12 1 0 -120 240 -120 20 -1 0 -720 1800 -1200 300 -30 1 0 -5040 |
| Alt | RevT(n, n - k), 0 ≤ k ≤ n | missing | 1 -1 0 1 -2 0 -1 6 -6 0 1 -12 36 -24 0 -1 20 -120 240 -120 0 1 -30 300 -1200 1800 -720 0 -1 42 -630 |
| Alt | InvT-1(n, k), 0 ≤ k ≤ n | missing | 1 0 1 0 2 1 0 -6 -6 1 0 -120 -108 12 1 0 1320 1200 -120 -20 1 0 65520 59400 -6000 -900 30 1 0 |
| Alt | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 0 1 2 0 1 -6 -6 0 1 12 -108 -120 0 1 -20 -120 1200 1320 0 1 30 -900 -6000 59400 65520 0 1 -42 |
| Alt | Accsee docs | missing | 1 0 -1 0 -2 -1 0 -6 0 -1 0 -24 12 0 1 0 -120 120 0 20 19 0 -720 1080 -120 180 150 151 0 -5040 10080 |
| Alt | AccRevsee docs | missing | 1 -1 -1 1 -1 -1 -1 5 -1 -1 1 -11 25 1 1 -1 19 -101 139 19 19 1 -29 271 -929 871 151 151 -1 41 -589 |
| Alt | AntiDiagsee docs | A180047 | 1 0 0 -1 0 -2 0 -6 1 0 -24 6 0 -120 36 -1 0 -720 240 -12 0 -5040 1800 -120 1 0 -40320 15120 -1200 |
| Alt | Diffx1T(n, k) (k+1) | A360205 | 1 0 -2 0 -4 3 0 -12 18 -4 0 -48 108 -48 5 0 -240 720 -480 100 -6 0 -1440 5400 -4800 1500 -180 7 0 |
| Alt | RowSum∑ k=0..n T(n, k) | A111884 | 1 -1 -1 -1 1 19 151 1091 7841 56519 396271 2442439 7701409 -145269541 -4833158329 -104056218421 |
| Alt | EvenSum∑ k=0..n T(n, k) even(k) | A088312 | 1 0 1 6 37 260 2101 19362 201097 2326536 29668681 413257790 6238931821 101415565836 1765092183037 |
| Alt | OddSum∑ k=0..n T(n, k) odd(k) | A088313 | 0 -1 -2 -7 -36 -241 -1950 -18271 -193256 -2270017 -29272410 -410815351 -6231230412 -101560835377 |
| Alt | AltSum∑ k=0..n T(n, k) (-1)^k | A000262 | 1 1 3 13 73 501 4051 37633 394353 4596553 58941091 824073141 12470162233 202976401213 3535017524403 |
| Alt | AbsSum∑ k=0..n | T(n, k) | | A000262 | 1 1 3 13 73 501 4051 37633 394353 4596553 58941091 824073141 12470162233 202976401213 3535017524403 |
| Alt | DiagSum∑ k=0..n // 2 T(n - k, k) | A058798 | 1 0 -1 -2 -5 -18 -85 -492 -3359 -26380 -234061 -2314230 -25222469 -300355398 -3879397705 |
| Alt | 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 |
| Alt | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A202410 | 1 -2 -1 2 17 94 487 2386 9473 638 -727729 -14280542 -222283631 -3235193378 -46058318473 |
| Alt | RowLcmLcm k=0..n | T(n, k) | > 1 | A359365 | 1 1 2 6 72 240 3600 75600 1411200 10160640 457228800 4191264000 184415616000 2054916864000 |
| Alt | RowGcdGcd k=0..n | T(n, k) | > 1 | A002378 | 1 1 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 | RowMaxMax k=0..n | T(n, k) | | A002868 | 1 1 2 6 36 240 1800 15120 141120 1693440 21772800 299376000 4390848000 68497228800 1133317785600 |
| Alt | ColMiddleT(n, n // 2) | A343581 | 1 0 -2 -6 36 240 -1200 -12600 58800 846720 -3810240 -69854400 307359360 6849722880 -29682132480 |
| Alt | CentralET(2 n, n) | A187535 | 1 -2 36 -1200 58800 -3810240 307359360 -29682132480 3339239904000 -428906814336000 |
| Alt | CentralOT(2 n + 1, n) | A367776 | 0 -6 240 -12600 846720 -69854400 6849722880 -779155977600 100919250432000 -14668613050291200 |
| 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) | A344050 | 1 -1 -3 -1 73 699 3001 -24697 -783999 -10946233 -80958779 656003919 40097528857 944102982419 |
| Alt | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A344051 | 1 -1 5 -37 361 -4301 60001 -954325 16984577 -333572041 7151967181 -165971975621 4139744524345 |
| Alt | TransNat0∑ k=0..n T(n, k) k | A317365 | 0 -1 0 3 16 75 336 1295 1632 -55881 -1124000 -16722981 -229985040 -3089923837 -41225160144 |
| Alt | TransNat1∑ k=0..n T(n, k) (k + 1) | A202410 | 1 -2 -1 2 17 94 487 2386 9473 638 -727729 -14280542 -222283631 -3235193378 -46058318473 |
| Alt | TransSqrs∑ k=0..n T(n, k) k^2 | A256467 | 0 -1 2 9 28 55 -234 -5047 -59464 -620433 -6210710 -60312791 -552386988 -4291343641 -14786103682 |
| Alt | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A318223 | 1 -1 -3 -13 -71 -441 -2699 -9157 206193 8443151 236126701 6169406979 161388751657 4327824442967 |
| Alt | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A025168 | 1 -1 5 -37 361 -4361 62701 -1044205 19748177 -417787921 9770678101 -250194150581 6959638411705 |
| 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) | A083374 | 0 -6 36 -120 300 -630 1176 -2016 3240 -4950 7260 -10296 14196 -19110 25200 -32640 41616 -52326 |
| Alt | DiagRow3T(n + 3, n) | A253285 | 0 -24 240 -1200 4200 -11760 28224 -60480 118800 -217800 377520 -624624 993720 -1528800 2284800 |
| Alt | DiagCol1T(n + 1, 1) | A000142 | -1 -2 -6 -24 -120 -720 -5040 -40320 -362880 -3628800 -39916800 -479001600 -6227020800 -87178291200 |
| Alt | DiagCol2T(n + 2, 2) | A001286 | 1 6 36 240 1800 15120 141120 1451520 16329600 199584000 2634508800 37362124800 566658892800 |
| Alt | DiagCol3T(n + 3, 3) | A001754 | -1 -12 -120 -1200 -12600 -141120 -1693440 -21772800 -299376000 -4390848000 -68497228800 |
| Alt | Polysee docs | missing | 1 0 1 0 -1 1 0 -1 -2 1 0 -1 0 -3 1 0 1 4 3 -4 1 0 19 16 9 8 -5 1 0 151 48 9 8 15 -6 1 0 1091 64 -63 |
| 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 -1 4 9 8 -5 -36 -91 -176 -297 -460 -671 -936 -1261 -1652 -2115 -2656 -3281 -3996 -4807 -5720 |
| Alt | PolyCol2∑ k=0..n T(n, k) 2^k | A317364 | 1 -2 0 4 16 48 64 -800 -12288 -127232 -1150976 -9266688 -58726400 -68777984 7510646784 207794409472 |
| Alt | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 -3 3 9 9 -63 -621 -3699 -14607 17253 1310499 20725713 249633657 2506512681 18706941171 |
| Alt | PolyDiag∑ k=0..n T(n, k) n^k | A317279 | 1 -1 0 9 -32 -225 3456 -2695 -433152 4495743 47872000 -1768142871 6703534080 597265448351 |
| Rev | TriangleT(n, k), 0 ≤ k ≤ n | missing | 1 1 0 1 2 0 1 6 6 0 1 12 36 24 0 1 20 120 240 120 0 1 30 300 1200 1800 720 0 1 42 630 4200 12600 |
| Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A271703 | 1 0 1 0 -2 1 0 6 -6 1 0 -24 36 -12 1 0 120 -240 120 -20 1 0 -720 1800 -1200 300 -30 1 0 5040 -15120 |
| Rev | Accsee docs | missing | 1 1 1 1 3 3 1 7 13 13 1 13 49 73 73 1 21 141 381 501 501 1 31 331 1531 3331 4051 4051 1 43 673 4873 |
| Rev | AccRevsee docs | A349776 | 1 0 1 0 2 3 0 6 12 13 0 24 60 72 73 0 120 360 480 500 501 0 720 2520 3720 4020 4050 4051 0 5040 |
| Rev | AntiDiagsee docs | missing | 1 1 1 0 1 2 1 6 0 1 12 6 1 20 36 0 1 30 120 24 1 42 300 240 0 1 56 630 1200 120 1 72 1176 4200 1800 |
| Rev | Diffx1T(n, k) (k+1) | missing | 1 1 0 1 4 0 1 12 18 0 1 24 108 96 0 1 40 360 960 600 0 1 60 900 4800 9000 4320 0 1 84 1890 16800 |
| Rev | RowSum∑ k=0..n T(n, k) | A000262 | 1 1 3 13 73 501 4051 37633 394353 4596553 58941091 824073141 12470162233 202976401213 3535017524403 |
| Rev | EvenSum∑ k=0..n T(n, k) even(k) | A096965 | 1 1 1 7 37 241 2101 18271 201097 2270017 29668681 410815351 6238931821 101560835377 1765092183037 |
| Rev | OddSum∑ k=0..n T(n, k) odd(k) | A096939 | 0 0 2 6 36 260 1950 19362 193256 2326536 29272410 413257790 6231230412 101415565836 1769925341366 |
| Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A111884 | 1 1 -1 1 1 -19 151 -1091 7841 -56519 396271 -2442439 7701409 145269541 -4833158329 104056218421 |
| Rev | AbsSum∑ k=0..n | T(n, k) | | A000262 | 1 1 3 13 73 501 4051 37633 394353 4596553 58941091 824073141 12470162233 202976401213 3535017524403 |
| Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 1 3 7 19 57 175 583 2007 7249 27187 105495 423403 1749097 7435479 32435527 145036735 663785793 |
| Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A002720 | 1 2 7 34 209 1546 13327 130922 1441729 17572114 234662231 3405357682 53334454417 896324308634 |
| Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A062147 | 1 1 5 31 229 1961 19081 207775 2501801 32989969 472630861 7307593151 121247816845 2148321709561 |
| Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | A359365 | 1 1 2 6 72 240 3600 75600 1411200 10160640 457228800 4191264000 184415616000 2054916864000 |
| Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | A002378 | 1 1 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 |
| Rev | RowMaxMax k=0..n | T(n, k) | | A002868 | 1 1 2 6 36 240 1800 15120 141120 1693440 21772800 299376000 4390848000 68497228800 1133317785600 |
| Rev | ColMiddleT(n, n // 2) | missing | 1 1 2 6 36 120 1200 4200 58800 211680 3810240 13970880 307359360 1141620480 29682132480 |
| Rev | CentralET(2 n, n) | A187535 | 1 2 36 1200 58800 3810240 307359360 29682132480 3339239904000 428906814336000 61934143990118400 |
| Rev | CentralOT(2 n + 1, n) | A248045 | 1 6 120 4200 211680 13970880 1141620480 111307996800 12614906304000 1629845894476800 |
| 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) | A344051 | 1 1 5 37 361 4301 60001 954325 16984577 333572041 7151967181 165971975621 4139744524345 |
| Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A344050 | 1 -1 -3 -1 73 699 3001 -24697 -783999 -10946233 -80958779 656003919 40097528857 944102982419 |
| Rev | TransNat0∑ k=0..n T(n, k) k | missing | 0 0 2 18 156 1460 15030 170142 2107448 28393416 413689770 6483520010 108777654612 1945345308348 |
| Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | A062147 | 1 1 5 31 229 1961 19081 207775 2501801 32989969 472630861 7307593151 121247816845 2148321709561 |
| Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 0 2 30 372 4580 58830 801402 11635400 180129672 2969097210 51989394710 964602295932 |
| Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A052897 | 1 2 8 44 304 2512 24064 261536 3173888 42483968 621159424 9841950208 167879268352 3065723549696 |
| Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A317364 | 1 -2 0 4 16 48 64 -800 -12288 -127232 -1150976 -9266688 -58726400 -68777984 7510646784 207794409472 |
| Rev | DiagRow1T(n + 1, n) | A000142 | 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 1307674368000 |
| Rev | DiagRow2T(n + 2, n) | A001286 | 1 6 36 240 1800 15120 141120 1451520 16329600 199584000 2634508800 37362124800 566658892800 |
| Rev | DiagRow3T(n + 3, n) | A001754 | 1 12 120 1200 12600 141120 1693440 21772800 299376000 4390848000 68497228800 1133317785600 |
| 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) | A083374 | 0 6 36 120 300 630 1176 2016 3240 4950 7260 10296 14196 19110 25200 32640 41616 52326 64980 79800 |
| Rev | DiagCol3T(n + 3, 3) | A253285 | 0 24 240 1200 4200 11760 28224 60480 118800 217800 377520 624624 993720 1528800 2284800 3329280 |
| Rev | Polysee docs | missing | 1 1 1 1 1 1 1 3 1 1 1 13 5 1 1 1 73 37 7 1 1 1 501 361 73 9 1 1 1 4051 4361 1009 121 11 1 1 1 37633 |
| 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 | A003154 | 1 13 37 73 121 181 253 337 433 541 661 793 937 1093 1261 1441 1633 1837 2053 2281 2521 2773 3037 |
| Rev | PolyCol2∑ k=0..n T(n, k) 2^k | A025168 | 1 1 5 37 361 4361 62701 1044205 19748177 417787921 9770678101 250194150581 6959638411705 |
| Rev | PolyCol3∑ k=0..n T(n, k) 3^k | A321837 | 1 1 7 73 1009 17341 355951 8488117 230439553 7013527129 236419161751 8740611892321 351566026652017 |
| Rev | PolyDiag∑ k=0..n T(n, k) n^k | A293146 | 1 1 5 73 2161 108101 8201701 878797165 126422091713 23514740267401 5492576235204901 |
| Inv | TriangleT(n, k), 0 ≤ k ≤ n | A271703 | 1 0 1 0 -2 1 0 6 -6 1 0 -24 36 -12 1 0 120 -240 120 -20 1 0 -720 1800 -1200 300 -30 1 0 5040 -15120 |
| Inv | RevT(n, n - k), 0 ≤ k ≤ n | missing | 1 1 0 1 -2 0 1 -6 6 0 1 -12 36 -24 0 1 -20 120 -240 120 0 1 -30 300 -1200 1800 -720 0 1 -42 630 |
| Inv | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 0 1 2 0 1 6 6 0 1 12 36 24 0 1 20 120 240 120 0 1 30 300 1200 1800 720 0 1 42 630 4200 12600 |
| Inv | Accsee docs | missing | 1 0 1 0 -2 -1 0 6 0 1 0 -24 12 0 1 0 120 -120 0 -20 -19 0 -720 1080 -120 180 150 151 0 5040 -10080 |
| Inv | AccRevsee docs | missing | 1 1 1 1 -1 -1 1 -5 1 1 1 -11 25 1 1 1 -19 101 -139 -19 -19 1 -29 271 -929 871 151 151 1 -41 589 |
| Inv | AntiDiagsee docs | A180047 | 1 0 0 1 0 -2 0 6 1 0 -24 -6 0 120 36 1 0 -720 -240 -12 0 5040 1800 120 1 0 -40320 -15120 -1200 -20 |
| Inv | Diffx1T(n, k) (k+1) | A360205 | 1 0 2 0 -4 3 0 12 -18 4 0 -48 108 -48 5 0 240 -720 480 -100 6 0 -1440 5400 -4800 1500 -180 7 0 |
| Inv | RowSum∑ k=0..n T(n, k) | A111884 | 1 1 -1 1 1 -19 151 -1091 7841 -56519 396271 -2442439 7701409 145269541 -4833158329 104056218421 |
| Inv | EvenSum∑ k=0..n T(n, k) even(k) | A088312 | 1 0 1 -6 37 -260 2101 -19362 201097 -2326536 29668681 -413257790 6238931821 -101415565836 |
| Inv | OddSum∑ k=0..n T(n, k) odd(k) | A088313 | 0 1 -2 7 -36 241 -1950 18271 -193256 2270017 -29272410 410815351 -6231230412 101560835377 |
| Inv | AltSum∑ k=0..n T(n, k) (-1)^k | A000262 | 1 -1 3 -13 73 -501 4051 -37633 394353 -4596553 58941091 -824073141 12470162233 -202976401213 |
| Inv | AbsSum∑ k=0..n | T(n, k) | | A000262 | 1 1 3 13 73 501 4051 37633 394353 4596553 58941091 824073141 12470162233 202976401213 3535017524403 |
| Inv | DiagSum∑ k=0..n // 2 T(n - k, k) | A001053 | 1 0 1 -2 7 -30 157 -972 6961 -56660 516901 -5225670 57999271 -701216922 9173819257 -129134686520 |
| Inv | 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 | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A202410 | 1 2 -1 -2 17 -94 487 -2386 9473 -638 -727729 14280542 -222283631 3235193378 -46058318473 |
| Inv | RowLcmLcm k=0..n | T(n, k) | > 1 | A359365 | 1 1 2 6 72 240 3600 75600 1411200 10160640 457228800 4191264000 184415616000 2054916864000 |
| Inv | RowGcdGcd k=0..n | T(n, k) | > 1 | A002378 | 1 1 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 | RowMaxMax k=0..n | T(n, k) | | A002868 | 1 1 2 6 36 240 1800 15120 141120 1693440 21772800 299376000 4390848000 68497228800 1133317785600 |
| Inv | ColMiddleT(n, n // 2) | A343581 | 1 0 -2 6 36 -240 -1200 12600 58800 -846720 -3810240 69854400 307359360 -6849722880 -29682132480 |
| Inv | CentralET(2 n, n) | A187535 | 1 -2 36 -1200 58800 -3810240 307359360 -29682132480 3339239904000 -428906814336000 |
| Inv | CentralOT(2 n + 1, n) | A367776 | 0 6 -240 12600 -846720 69854400 -6849722880 779155977600 -100919250432000 14668613050291200 |
| 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) | A344050 | 1 1 -3 1 73 -699 3001 24697 -783999 10946233 -80958779 -656003919 40097528857 -944102982419 |
| Inv | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A344051 | 1 1 5 37 361 4301 60001 954325 16984577 333572041 7151967181 165971975621 4139744524345 |
| Inv | TransNat0∑ k=0..n T(n, k) k | A317365 | 0 1 0 -3 16 -75 336 -1295 1632 55881 -1124000 16722981 -229985040 3089923837 -41225160144 |
| Inv | TransNat1∑ k=0..n T(n, k) (k + 1) | A202410 | 1 2 -1 -2 17 -94 487 -2386 9473 -638 -727729 14280542 -222283631 3235193378 -46058318473 |
| Inv | TransSqrs∑ k=0..n T(n, k) k^2 | A256467 | 0 1 2 -9 28 -55 -234 5047 -59464 620433 -6210710 60312791 -552386988 4291343641 -14786103682 |
| Inv | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A318223 | 1 1 -3 13 -71 441 -2699 9157 206193 -8443151 236126701 -6169406979 161388751657 -4327824442967 |
| Inv | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A025168 | 1 1 5 37 361 4361 62701 1044205 19748177 417787921 9770678101 250194150581 6959638411705 |
| 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) | A083374 | 0 6 36 120 300 630 1176 2016 3240 4950 7260 10296 14196 19110 25200 32640 41616 52326 64980 79800 |
| Inv | DiagRow3T(n + 3, n) | A253285 | 0 -24 -240 -1200 -4200 -11760 -28224 -60480 -118800 -217800 -377520 -624624 -993720 -1528800 |
| Inv | DiagCol1T(n + 1, 1) | A000142 | 1 -2 6 -24 120 -720 5040 -40320 362880 -3628800 39916800 -479001600 6227020800 -87178291200 |
| Inv | DiagCol2T(n + 2, 2) | A001286 | 1 -6 36 -240 1800 -15120 141120 -1451520 16329600 -199584000 2634508800 -37362124800 566658892800 |
| Inv | DiagCol3T(n + 3, 3) | A001754 | 1 -12 120 -1200 12600 -141120 1693440 -21772800 299376000 -4390848000 68497228800 -1133317785600 |
| Inv | Polysee docs | missing | 1 0 1 0 1 1 0 -1 2 1 0 1 0 3 1 0 1 -4 3 4 1 0 -19 16 -9 8 5 1 0 151 -48 9 -8 15 6 1 0 -1091 64 63 |
| 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 | missing | 0 1 -4 -9 -8 5 36 91 176 297 460 671 936 1261 1652 2115 2656 3281 3996 4807 5720 6741 7876 9131 |
| Inv | PolyCol2∑ k=0..n T(n, k) 2^k | A317364 | 1 2 0 -4 16 -48 64 800 -12288 127232 -1150976 9266688 -58726400 68777984 7510646784 -207794409472 |
| Inv | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 3 3 -9 9 63 -621 3699 -14607 -17253 1310499 -20725713 249633657 -2506512681 18706941171 |
| Inv | PolyDiag∑ k=0..n T(n, k) n^k | A317279 | 1 1 0 -9 -32 225 3456 2695 -433152 -4495743 47872000 1768142871 6703534080 -597265448351 |
| Inv:Rev | TriangleT(n, k), 0 ≤ k ≤ n | missing | 1 1 0 1 -2 0 1 -6 6 0 1 -12 36 -24 0 1 -20 120 -240 120 0 1 -30 300 -1200 1800 -720 0 1 -42 630 |
| Inv:Rev | RevT(n, n - k), 0 ≤ k ≤ n | A271703 | 1 0 1 0 -2 1 0 6 -6 1 0 -24 36 -12 1 0 120 -240 120 -20 1 0 -720 1800 -1200 300 -30 1 0 5040 -15120 |
| Inv:Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A271703 | 1 0 1 0 2 1 0 6 6 1 0 24 36 12 1 0 120 240 120 20 1 0 720 1800 1200 300 30 1 0 5040 15120 12600 |
| Inv:Rev | Accsee docs | missing | 1 1 1 1 -1 -1 1 -5 1 1 1 -11 25 1 1 1 -19 101 -139 -19 -19 1 -29 271 -929 871 151 151 1 -41 589 |
| Inv:Rev | AccRevsee docs | missing | 1 0 1 0 -2 -1 0 6 0 1 0 -24 12 0 1 0 120 -120 0 -20 -19 0 -720 1080 -120 180 150 151 0 5040 -10080 |
| Inv:Rev | AntiDiagsee docs | missing | 1 1 1 0 1 -2 1 -6 0 1 -12 6 1 -20 36 0 1 -30 120 -24 1 -42 300 -240 0 1 -56 630 -1200 120 1 -72 |
| Inv:Rev | Diffx1T(n, k) (k+1) | missing | 1 1 0 1 -4 0 1 -12 18 0 1 -24 108 -96 0 1 -40 360 -960 600 0 1 -60 900 -4800 9000 -4320 0 1 -84 |
| Inv:Rev | RowSum∑ k=0..n T(n, k) | A111884 | 1 1 -1 1 1 -19 151 -1091 7841 -56519 396271 -2442439 7701409 145269541 -4833158329 104056218421 |
| Inv:Rev | EvenSum∑ k=0..n T(n, k) even(k) | A096965 | 1 1 1 7 37 241 2101 18271 201097 2270017 29668681 410815351 6238931821 101560835377 1765092183037 |
| Inv:Rev | OddSum∑ k=0..n T(n, k) odd(k) | A096939 | 0 0 -2 -6 -36 -260 -1950 -19362 -193256 -2326536 -29272410 -413257790 -6231230412 -101415565836 |
| Inv:Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A000262 | 1 1 3 13 73 501 4051 37633 394353 4596553 58941091 824073141 12470162233 202976401213 3535017524403 |
| Inv:Rev | AbsSum∑ k=0..n | T(n, k) | | A000262 | 1 1 3 13 73 501 4051 37633 394353 4596553 58941091 824073141 12470162233 202976401213 3535017524403 |
| Inv:Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 1 -1 -5 -5 17 67 19 -505 -1295 2047 18587 19939 -182255 -701605 835267 12424447 17996849 |
| Inv:Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A202410 | 1 2 -1 -2 17 -94 487 -2386 9473 -638 -727729 14280542 -222283631 3235193378 -46058318473 |
| Inv:Rev | 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:Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | A359365 | 1 1 2 6 72 240 3600 75600 1411200 10160640 457228800 4191264000 184415616000 2054916864000 |
| Inv:Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | A002378 | 1 1 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:Rev | RowMaxMax k=0..n | T(n, k) | | A002868 | 1 1 2 6 36 240 1800 15120 141120 1693440 21772800 299376000 4390848000 68497228800 1133317785600 |
| Inv:Rev | ColMiddleT(n, n // 2) | missing | 1 1 -2 -6 36 120 -1200 -4200 58800 211680 -3810240 -13970880 307359360 1141620480 -29682132480 |
| Inv:Rev | CentralET(2 n, n) | A187535 | 1 -2 36 -1200 58800 -3810240 307359360 -29682132480 3339239904000 -428906814336000 |
| Inv:Rev | CentralOT(2 n + 1, n) | A248045 | 1 -6 120 -4200 211680 -13970880 1141620480 -111307996800 12614906304000 -1629845894476800 |
| 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) | A344050 | 1 1 -3 1 73 -699 3001 24697 -783999 10946233 -80958779 -656003919 40097528857 -944102982419 |
| Inv:Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A344051 | 1 -1 5 -37 361 -4301 60001 -954325 16984577 -333572041 7151967181 -165971975621 4139744524345 |
| Inv:Rev | TransNat0∑ k=0..n T(n, k) k | missing | 0 0 -2 6 -12 -20 570 -6342 61096 -564552 5086710 -43589810 322401948 -1201419804 -26439056462 |
| Inv:Rev | 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:Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 0 -2 18 -84 220 1170 -30282 416248 -4963464 55896390 -603127910 6076256868 -51496123692 |
| Inv:Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A317364 | 1 2 0 -4 16 -48 64 800 -12288 127232 -1150976 9266688 -58726400 68777984 7510646784 -207794409472 |
| Inv:Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A052897 | 1 -2 8 -44 304 -2512 24064 -261536 3173888 -42483968 621159424 -9841950208 167879268352 |
| Inv:Rev | DiagRow1T(n + 1, n) | A000142 | 1 -2 6 -24 120 -720 5040 -40320 362880 -3628800 39916800 -479001600 6227020800 -87178291200 |
| Inv:Rev | DiagRow2T(n + 2, n) | A001286 | 1 -6 36 -240 1800 -15120 141120 -1451520 16329600 -199584000 2634508800 -37362124800 566658892800 |
| Inv:Rev | DiagRow3T(n + 3, n) | A001754 | 1 -12 120 -1200 12600 -141120 1693440 -21772800 299376000 -4390848000 68497228800 -1133317785600 |
| 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) | A083374 | 0 6 36 120 300 630 1176 2016 3240 4950 7260 10296 14196 19110 25200 32640 41616 52326 64980 79800 |
| Inv:Rev | DiagCol3T(n + 3, 3) | A253285 | 0 -24 -240 -1200 -4200 -11760 -28224 -60480 -118800 -217800 -377520 -624624 -993720 -1528800 |
| Inv:Rev | Polysee docs | missing | 1 1 1 1 1 1 1 -1 1 1 1 1 -3 1 1 1 1 13 -5 1 1 1 -19 -71 37 -7 1 1 1 151 441 -359 73 -9 1 1 1 -1091 |
| 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 | A003154 | 1 1 13 37 73 121 181 253 337 433 541 661 793 937 1093 1261 1441 1633 1837 2053 2281 2521 2773 3037 |
| Inv:Rev | PolyCol2∑ k=0..n T(n, k) 2^k | A318223 | 1 1 -3 13 -71 441 -2699 9157 206193 -8443151 236126701 -6169406979 161388751657 -4327824442967 |
| Inv:Rev | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 1 -5 37 -359 4261 -58949 912745 -15139823 251548201 -3521449349 4011468781 3225489384745 |
| Inv:Rev | PolyDiag∑ k=0..n T(n, k) n^k | A318224 | 1 1 -3 37 -1007 47901 -3514499 367671697 -51952729023 9529552851193 -2201241933756899 |
| << | 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.