OEIS Similars: A028246, A053440, A075263, A130850, A163626
| ↕ Type | ↕ Trait | ↕ Anum | ↕ Sequence |
|---|---|---|---|
| Std | TriangleT(n, k), 0 ≤ k ≤ n | A028246 | 1 1 1 1 3 2 1 7 12 6 1 15 50 60 24 1 31 180 390 360 120 1 63 602 2100 3360 2520 720 1 127 1932 |
| Std | RevT(n, n - k), 0 ≤ k ≤ n | A130850 | 1 1 1 2 3 1 6 12 7 1 24 60 50 15 1 120 360 390 180 31 1 720 2520 3360 2100 602 63 1 5040 20160 |
| Std | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A106340 | 1 -1 1 1 -3 1 -1 9 -7 1 1 -45 55 -15 1 -1 585 -835 285 -31 1 1 -21105 30835 -11025 1351 -63 1 -1 |
| Std | Accsee docs | missing | 1 1 2 1 4 6 1 8 20 26 1 16 66 126 150 1 32 212 602 962 1082 1 64 666 2766 6126 8646 9366 1 128 2060 |
| Std | AccRevsee docs | A054255 | 1 1 2 2 5 6 6 18 25 26 24 84 134 149 150 120 480 870 1050 1081 1082 720 3240 6600 8700 9302 9365 |
| Std | AntiDiagsee docs | missing | 1 1 1 1 1 3 1 7 2 1 15 12 1 31 50 6 1 63 180 60 1 127 602 390 24 1 255 1932 2100 360 1 511 6050 |
| Std | Diffx1T(n, k) (k+1) | A019538 | 1 1 2 1 6 6 1 14 36 24 1 30 150 240 120 1 62 540 1560 1800 720 1 126 1806 8400 16800 15120 5040 1 |
| Std | RowSum∑ k=0..n T(n, k) | A000629 | 1 2 6 26 150 1082 9366 94586 1091670 14174522 204495126 3245265146 56183135190 1053716696762 |
| Std | EvenSum∑ k=0..n T(n, k) even(k) | A000670 | 1 1 3 13 75 541 4683 47293 545835 7087261 102247563 1622632573 28091567595 526858348381 |
| Std | OddSum∑ k=0..n T(n, k) odd(k) | A000670 | 0 1 3 13 75 541 4683 47293 545835 7087261 102247563 1622632573 28091567595 526858348381 |
| Std | AltSum∑ k=0..n T(n, k) (-1)^k | 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 | AbsSum∑ k=0..n | T(n, k) | | A000629 | 1 2 6 26 150 1082 9366 94586 1091670 14174522 204495126 3245265146 56183135190 1053716696762 |
| Std | DiagSum∑ k=0..n // 2 T(n - k, k) | A229046 | 1 1 2 4 10 28 88 304 1144 4648 20248 94024 463144 2409928 13198888 75848584 456066664 2862257608 |
| Std | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 3 11 55 359 2891 27635 305439 3829439 53672179 831308939 14096879303 259705544279 5164407480987 |
| Std | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A000670 | 1 3 13 75 541 4683 47293 545835 7087261 102247563 1622632573 28091567595 526858348381 |
| Std | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 6 84 600 145080 2167200 453138235200 319959556963200 481032520489720080000 |
| Std | RowGcdGcd k=0..n | T(n, k) | > 1 | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Std | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 3 12 60 390 3360 31920 332640 4233600 59875200 898128000 14495120640 273158645760 5368729766400 |
| Std | ColMiddleT(n, n // 2) | missing | 1 1 3 7 50 180 2100 10206 166824 1020600 21538440 158838240 4115105280 35517081600 1091804313600 |
| Std | CentralET(2 n, n) | A185157 | 1 3 50 2100 166824 21538440 4115105280 1091804313600 384202115256960 173201547619900800 |
| Std | CentralOT(2 n + 1, n) | missing | 1 7 180 10206 1020600 158838240 35517081600 10794490827120 4280991956841600 2147373231974006400 |
| Std | ColLeftT(n, 0) | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Std | ColRightT(n, n) | A000142 | 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 |
| Std | BinConv∑ k=0..n C(n, k) T(n, k) | A000169 | 1 2 9 64 625 7776 117649 2097152 43046721 1000000000 25937424601 743008370688 23298085122481 |
| Std | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A343584 | 1 0 -3 -10 25 574 2653 -30234 -644079 -2438722 102934381 2094370486 680814121 -762930678498 |
| Std | TransNat0∑ k=0..n T(n, k) k | A343583 | 0 1 7 49 391 3601 37927 451249 5995591 88073041 1418137447 24846302449 470675213191 9587626273681 |
| Std | TransNat1∑ k=0..n T(n, k) (k + 1) | A000670 | 1 3 13 75 541 4683 47293 545835 7087261 102247563 1622632573 28091567595 526858348381 |
| Std | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 11 109 1139 13021 164051 2273629 34497299 569871901 10193697491 196445520349 4059708749459 |
| Std | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A123227 | 1 3 12 66 480 4368 47712 608016 8855040 145083648 2641216512 52891055616 1155444326400 |
| Std | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A009006 | 1 -1 0 2 0 -16 0 272 0 -7936 0 353792 0 -22368256 0 1903757312 0 -209865342976 0 29088885112832 0 |
| Std | DiagRow1T(n + 1, n) | A001710 | 1 3 12 60 360 2520 20160 181440 1814400 19958400 239500800 3113510400 43589145600 653837184000 |
| Std | DiagRow2T(n + 2, n) | A005460 | 1 7 50 390 3360 31920 332640 3780000 46569600 618710400 8821612800 134399865600 2179457280000 |
| Std | DiagRow3T(n + 3, n) | A005461 | 1 15 180 2100 25200 317520 4233600 59875200 898128000 14270256000 239740300800 4249941696000 |
| Std | DiagCol1T(n + 1, 1) | A000225 | 1 3 7 15 31 63 127 255 511 1023 2047 4095 8191 16383 32767 65535 131071 262143 524287 1048575 |
| Std | DiagCol2T(n + 2, 2) | A028243 | 2 12 50 180 602 1932 6050 18660 57002 173052 523250 1577940 4750202 14283372 42915650 128878020 |
| Std | DiagCol3T(n + 3, 3) | A028244 | 6 60 390 2100 10206 46620 204630 874500 3669006 15195180 62350470 254135700 1030793406 4166023740 |
| Std | Polysee docs | A369435 | 1 1 1 1 2 1 1 6 3 1 1 26 15 4 1 1 150 111 28 5 1 1 1082 1095 292 45 6 1 1 9366 13503 4060 605 66 7 |
| 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 | A000384 | 1 6 15 28 45 66 91 120 153 190 231 276 325 378 435 496 561 630 703 780 861 946 1035 1128 1225 1326 |
| Std | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 1 26 111 292 605 1086 1771 2696 3897 5410 7271 9516 12181 15302 18915 23056 27761 33066 39007 45620 |
| Std | PolyCol2∑ k=0..n T(n, k) 2^k | A201339 | 1 3 15 111 1095 13503 199815 3449631 68062695 1510769343 37260156615 1010843385951 29916558512295 |
| Std | PolyCol3∑ k=0..n T(n, k) 3^k | A201354 | 1 4 28 292 4060 70564 1471708 35810212 995827420 31153998244 1082931514588 41407678132132 |
| Std | PolyDiag∑ k=0..n T(n, k) n^k | A372312 | 1 2 15 292 10845 653406 58018051 7123041416 1155276253305 239189245299010 61550396579410431 |
| Alt | TriangleT(n, k), 0 ≤ k ≤ n | A028246 | 1 1 -1 1 -3 2 1 -7 12 -6 1 -15 50 -60 24 1 -31 180 -390 360 -120 1 -63 602 -2100 3360 -2520 720 1 |
| Alt | RevT(n, n - k), 0 ≤ k ≤ n | A130850 | 1 -1 1 2 -3 1 -6 12 -7 1 24 -60 50 -15 1 -120 360 -390 180 -31 1 720 -2520 3360 -2100 602 -63 1 |
| Alt | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A106340 | 1 1 1 1 3 1 1 9 7 1 1 45 55 15 1 1 585 835 285 31 1 1 21105 30835 11025 1351 63 1 1 1858185 2719675 |
| Alt | Accsee docs | missing | 1 1 0 1 -2 0 1 -6 6 0 1 -14 36 -24 0 1 -30 150 -240 120 0 1 -62 540 -1560 1800 -720 0 1 -126 1806 |
| Alt | AntiDiagsee docs | missing | 1 1 1 -1 1 -3 1 -7 2 1 -15 12 1 -31 50 -6 1 -63 180 -60 1 -127 602 -390 24 1 -255 1932 -2100 360 1 |
| Alt | RowSum∑ k=0..n T(n, k) | 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 | EvenSum∑ k=0..n T(n, k) even(k) | A000670 | 1 1 3 13 75 541 4683 47293 545835 7087261 102247563 1622632573 28091567595 526858348381 |
| Alt | OddSum∑ k=0..n T(n, k) odd(k) | A000670 | 0 -1 -3 -13 -75 -541 -4683 -47293 -545835 -7087261 -102247563 -1622632573 -28091567595 |
| Alt | AltSum∑ k=0..n T(n, k) (-1)^k | A000629 | 1 2 6 26 150 1082 9366 94586 1091670 14174522 204495126 3245265146 56183135190 1053716696762 |
| Alt | AbsSum∑ k=0..n | T(n, k) | | A000629 | 1 2 6 26 150 1082 9366 94586 1091670 14174522 204495126 3245265146 56183135190 1053716696762 |
| Alt | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 0 -2 -4 -2 14 58 110 -62 -1426 -6302 -14050 17698 355934 1985698 6063710 -3010142 -182151586 |
| Alt | AccSum∑ k=0..n ∑ j=0..k T(n, j) | 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 |
| Alt | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 6 84 600 145080 2167200 453138235200 319959556963200 481032520489720080000 |
| Alt | RowGcdGcd k=0..n | T(n, k) | > 1 | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Alt | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 3 12 60 390 3360 31920 332640 4233600 59875200 898128000 14495120640 273158645760 5368729766400 |
| Alt | ColMiddleT(n, n // 2) | missing | 1 1 -3 -7 50 180 -2100 -10206 166824 1020600 -21538440 -158838240 4115105280 35517081600 |
| Alt | CentralET(2 n, n) | A185157 | 1 -3 50 -2100 166824 -21538440 4115105280 -1091804313600 384202115256960 -173201547619900800 |
| Alt | CentralOT(2 n + 1, n) | missing | 1 -7 180 -10206 1020600 -158838240 35517081600 -10794490827120 4280991956841600 |
| Alt | ColLeftT(n, 0) | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Alt | ColRightT(n, n) | 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) | A343584 | 1 0 -3 10 25 -574 2653 30234 -644079 2438722 102934381 -2094370486 680814121 762930678498 |
| Alt | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A000169 | 1 -2 9 -64 625 -7776 117649 -2097152 43046721 -1000000000 25937424601 -743008370688 23298085122481 |
| Alt | TransNat0∑ k=0..n T(n, k) k | A000012 | 0 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 |
| Alt | TransSqrs∑ k=0..n T(n, k) k^2 | A036563 | 0 -1 5 -13 29 -61 125 -253 509 -1021 2045 -4093 8189 -16381 32765 -65533 131069 -262141 524285 |
| Alt | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A009006 | 1 1 0 -2 0 16 0 -272 0 7936 0 -353792 0 22368256 0 -1903757312 0 209865342976 0 -29088885112832 0 |
| Alt | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A123227 | 1 -3 12 -66 480 -4368 47712 -608016 8855040 -145083648 2641216512 -52891055616 1155444326400 |
| Alt | DiagRow1T(n + 1, n) | A001710 | 1 -3 12 -60 360 -2520 20160 -181440 1814400 -19958400 239500800 -3113510400 43589145600 |
| Alt | DiagRow2T(n + 2, n) | A005460 | 1 -7 50 -390 3360 -31920 332640 -3780000 46569600 -618710400 8821612800 -134399865600 2179457280000 |
| Alt | DiagRow3T(n + 3, n) | A005461 | 1 -15 180 -2100 25200 -317520 4233600 -59875200 898128000 -14270256000 239740300800 -4249941696000 |
| Alt | DiagCol1T(n + 1, 1) | A000225 | -1 -3 -7 -15 -31 -63 -127 -255 -511 -1023 -2047 -4095 -8191 -16383 -32767 -65535 -131071 -262143 |
| Alt | DiagCol2T(n + 2, 2) | A028243 | 2 12 50 180 602 1932 6050 18660 57002 173052 523250 1577940 4750202 14283372 42915650 128878020 |
| Alt | DiagCol3T(n + 3, 3) | A028244 | -6 -60 -390 -2100 -10206 -46620 -204630 -874500 -3669006 -15195180 -62350470 -254135700 -1030793406 |
| Alt | Polysee docs | missing | 1 1 1 1 0 1 1 0 -1 1 1 0 3 -2 1 1 0 -13 10 -3 1 1 0 75 -74 21 -4 1 1 0 -541 730 -219 36 -5 1 1 0 |
| 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 | A014105 | 1 0 3 10 21 36 55 78 105 136 171 210 253 300 351 406 465 528 595 666 741 820 903 990 1081 1176 1275 |
| Alt | PolyRow3∑ k=0..3 T(3, k) n^k | A094421 | 1 0 -13 -74 -219 -484 -905 -1518 -2359 -3464 -4869 -6610 -8723 -11244 -14209 -17654 -21615 -26128 |
| Alt | PolyCol2∑ k=0..n T(n, k) 2^k | A000670 | 1 -1 3 -13 75 -541 4683 -47293 545835 -7087261 102247563 -1622632573 28091567595 -526858348381 |
| Alt | PolyCol3∑ k=0..n T(n, k) 3^k | A004123 | 1 -2 10 -74 730 -9002 133210 -2299754 45375130 -1007179562 24840104410 -673895590634 19944372341530 |
| Alt | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 0 3 -74 3045 -194404 17919055 -2258233998 373405001865 -78468091562888 20431783142389971 |
| Rev | TriangleT(n, k), 0 ≤ k ≤ n | A130850 | 1 1 1 2 3 1 6 12 7 1 24 60 50 15 1 120 360 390 180 31 1 720 2520 3360 2100 602 63 1 5040 20160 |
| Rev | InvT-1(n, k), 0 ≤ k ≤ n | A106340 | 1 -1 1 1 -3 1 -1 9 -7 1 1 -45 55 -15 1 -1 585 -835 285 -31 1 1 -21105 30835 -11025 1351 -63 1 -1 |
| Rev | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 -1 1 -3 1 1 -7 9 -1 1 -15 55 -45 1 1 -31 285 -835 585 -1 1 -63 1351 -11025 30835 -21105 1 1 |
| Rev | Accsee docs | A054255 | 1 1 2 2 5 6 6 18 25 26 24 84 134 149 150 120 480 870 1050 1081 1082 720 3240 6600 8700 9302 9365 |
| Rev | AccRevsee docs | missing | 1 1 2 1 4 6 1 8 20 26 1 16 66 126 150 1 32 212 602 962 1082 1 64 666 2766 6126 8646 9366 1 128 2060 |
| Rev | AntiDiagsee docs | missing | 1 1 2 1 6 3 24 12 1 120 60 7 720 360 50 1 5040 2520 390 15 40320 20160 3360 180 1 362880 181440 |
| Rev | Diffx1T(n, k) (k+1) | missing | 1 1 2 2 6 3 6 24 21 4 24 120 150 60 5 120 720 1170 720 155 6 720 5040 10080 8400 3010 378 7 5040 |
| Rev | RowSum∑ k=0..n T(n, k) | A000629 | 1 2 6 26 150 1082 9366 94586 1091670 14174522 204495126 3245265146 56183135190 1053716696762 |
| Rev | EvenSum∑ k=0..n T(n, k) even(k) | A000670 | 1 1 3 13 75 541 4683 47293 545835 7087261 102247563 1622632573 28091567595 526858348381 |
| Rev | OddSum∑ k=0..n T(n, k) odd(k) | A000670 | 0 1 3 13 75 541 4683 47293 545835 7087261 102247563 1622632573 28091567595 526858348381 |
| Rev | AltSum∑ k=0..n T(n, k) (-1)^k | 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 | AbsSum∑ k=0..n | T(n, k) | | A000629 | 1 2 6 26 150 1082 9366 94586 1091670 14174522 204495126 3245265146 56183135190 1053716696762 |
| Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 3 9 37 187 1131 7965 64021 578371 5801643 63982989 769474357 10021902787 140534274891 |
| Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A000670 | 1 3 13 75 541 4683 47293 545835 7087261 102247563 1622632573 28091567595 526858348381 |
| Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 3 11 55 359 2891 27635 305439 3829439 53672179 831308939 14096879303 259705544279 5164407480987 |
| Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 6 84 600 145080 2167200 453138235200 319959556963200 481032520489720080000 |
| Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Rev | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 3 12 60 390 3360 31920 332640 4233600 59875200 898128000 14495120640 273158645760 5368729766400 |
| Rev | ColMiddleT(n, n // 2) | missing | 1 1 3 12 50 390 2100 25200 166824 2739240 21538440 451725120 4115105280 105398092800 1091804313600 |
| Rev | CentralET(2 n, n) | A185157 | 1 3 50 2100 166824 21538440 4115105280 1091804313600 384202115256960 173201547619900800 |
| Rev | CentralOT(2 n + 1, n) | missing | 1 12 390 25200 2739240 451725120 105398092800 33094020960000 13467262000832640 6897777008118796800 |
| Rev | ColLeftT(n, 0) | A000142 | 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 |
| Rev | ColRightT(n, n) | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Rev | BinConv∑ k=0..n C(n, k) T(n, k) | A000169 | 1 2 9 64 625 7776 117649 2097152 43046721 1000000000 25937424601 743008370688 23298085122481 |
| Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A343584 | 1 0 -3 10 25 -574 2653 30234 -644079 2438722 102934381 -2094370486 680814121 762930678498 |
| Rev | TransNat0∑ k=0..n T(n, k) k | missing | 0 1 5 29 209 1809 18269 210853 2737769 39497657 626813813 10851614157 203522409089 4110690784225 |
| Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 3 11 55 359 2891 27635 305439 3829439 53672179 831308939 14096879303 259705544279 5164407480987 |
| Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 7 49 411 4061 46103 590857 8434723 132693445 2280461151 42503949137 853875100235 18391793396653 |
| Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A201339 | 1 3 15 111 1095 13503 199815 3449631 68062695 1510769343 37260156615 1010843385951 29916558512295 |
| Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A000670 | 1 -1 3 -13 75 -541 4683 -47293 545835 -7087261 102247563 -1622632573 28091567595 -526858348381 |
| Rev | DiagRow1T(n + 1, n) | A000225 | 1 3 7 15 31 63 127 255 511 1023 2047 4095 8191 16383 32767 65535 131071 262143 524287 1048575 |
| Rev | DiagRow2T(n + 2, n) | A028243 | 2 12 50 180 602 1932 6050 18660 57002 173052 523250 1577940 4750202 14283372 42915650 128878020 |
| Rev | DiagRow3T(n + 3, n) | A028244 | 6 60 390 2100 10206 46620 204630 874500 3669006 15195180 62350470 254135700 1030793406 4166023740 |
| Rev | DiagCol1T(n + 1, 1) | A001710 | 1 3 12 60 360 2520 20160 181440 1814400 19958400 239500800 3113510400 43589145600 653837184000 |
| Rev | DiagCol2T(n + 2, 2) | A005460 | 1 7 50 390 3360 31920 332640 3780000 46569600 618710400 8821612800 134399865600 2179457280000 |
| Rev | DiagCol3T(n + 3, 3) | A005461 | 1 15 180 2100 25200 317520 4233600 59875200 898128000 14270256000 239740300800 4249941696000 |
| Rev | Polysee docs | missing | 1 1 1 2 2 1 6 6 3 1 24 26 12 4 1 120 150 66 20 5 1 720 1082 480 132 30 6 1 5040 9366 4368 1140 230 |
| 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 | A002378 | 2 6 12 20 30 42 56 72 90 110 132 156 182 210 240 272 306 342 380 420 462 506 552 600 650 702 756 |
| Rev | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 6 26 66 132 230 366 546 776 1062 1410 1826 2316 2886 3542 4290 5136 6086 7146 8322 9620 11046 12606 |
| Rev | PolyCol2∑ k=0..n T(n, k) 2^k | A123227 | 1 3 12 66 480 4368 47712 608016 8855040 145083648 2641216512 52891055616 1155444326400 |
| Rev | PolyCol3∑ k=0..n T(n, k) 3^k | A201355 | 1 4 20 132 1140 12324 160020 2424132 41967540 817374564 17688328020 421061260932 10934334077940 |
| Rev | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 2 12 132 2280 56670 1907136 83094536 4533828480 302029998210 24079005772800 2260195356904716 |
| Rev:Inv | TriangleT(n, k), 0 ≤ k ≤ n | A106340 | 1 -1 1 1 -3 1 -1 9 -7 1 1 -45 55 -15 1 -1 585 -835 285 -31 1 1 -21105 30835 -11025 1351 -63 1 -1 |
| Rev:Inv | RevT(n, n - k), 0 ≤ k ≤ n | missing | 1 1 -1 1 -3 1 1 -7 9 -1 1 -15 55 -45 1 1 -31 285 -835 585 -1 1 -63 1351 -11025 30835 -21105 1 1 |
| Rev:Inv | InvT-1(n, k), 0 ≤ k ≤ n | A130850 | 1 1 1 2 3 1 6 12 7 1 24 60 50 15 1 120 360 390 180 31 1 720 2520 3360 2100 602 63 1 5040 20160 |
| Rev:Inv | RevInvT-1(n, n - k), 0 ≤ k ≤ n | A028246 | 1 1 1 1 3 2 1 7 12 6 1 15 50 60 24 1 31 180 390 360 120 1 63 602 2100 3360 2520 720 1 127 1932 |
| Rev:Inv | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | missing | 1 -1 1 -4 3 1 28 -20 -9 1 1464 -1050 -460 45 1 -831952 596726 261300 -25490 -585 1 -17603175360 |
| Rev:Inv | Accsee docs | missing | 1 -1 0 1 -2 -1 -1 8 1 2 1 -44 11 -4 -3 -1 584 -251 34 3 4 1 -21104 9731 -1294 57 -6 -5 -1 1858184 |
| Rev:Inv | AccRevsee docs | missing | 1 1 0 1 -2 -1 1 -6 3 2 1 -14 41 -4 -3 1 -30 255 -580 5 4 1 -62 1289 -9736 21099 -6 -5 1 -126 5943 |
| Rev:Inv | AntiDiagsee docs | missing | 1 -1 1 1 -1 -3 1 9 1 -1 -45 -7 1 585 55 1 -1 -21105 -835 -15 1 1858185 30835 285 1 -1 -367958745 |
| Rev:Inv | Diffx1T(n, k) (k+1) | missing | 1 -1 2 1 -6 3 -1 18 -21 4 1 -90 165 -60 5 -1 1170 -2505 1140 -155 6 1 -42210 92505 -44100 6755 -378 |
| Rev:Inv | RowSum∑ k=0..n T(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 |
| Rev:Inv | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 -1 2 -8 57 -867 32188 -2841694 562821143 -240405740633 216164051384514 -402860797699465140 |
| Rev:Inv | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 1 -3 10 -60 871 -32193 2841700 -562821150 240405740641 -216164051384523 402860797699465150 |
| Rev:Inv | AltSum∑ k=0..n T(n, k) (-1)^k | missing | 1 -2 5 -18 117 -1738 64381 -5683394 1125642293 -480811481274 432328102769037 -805721595398930290 |
| Rev:Inv | AbsSum∑ k=0..n | T(n, k) | | missing | 1 2 5 18 117 1738 64381 5683394 1125642293 480811481274 432328102769037 805721595398930290 |
| Rev:Inv | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 -1 2 -4 11 -53 642 -21956 1889307 -370689477 157709127298 -141551266403940 263584195784100907 |
| Rev:Inv | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 -1 -2 10 -39 373 -12620 1106852 -219148685 93606371383 -84167343442434 156861056845864270 |
| Rev:Inv | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 1 -2 0 21 -345 12580 -1106798 219148615 -93606371295 84167343442326 -156861056845864140 |
| Rev:Inv | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 3 63 495 57542355 125599126275 16844027146592997737925 4147431491472964184928637039792321755 |
| Rev:Inv | RowGcdGcd k=0..n | T(n, k) | > 1 | A089026 | 1 1 3 1 5 1 7 1 1 1 11 1 13 1 1 1 17 1 19 1 1 1 23 1 1 1 1 1 29 1 31 1 1 1 1 1 37 1 1 1 41 1 43 1 1 |
| Rev:Inv | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 3 9 55 835 30835 2719675 538607755 230061795355 206863086384955 385526761633044955 |
| Rev:Inv | ColMiddleT(n, n // 2) | missing | 1 -1 -3 9 55 -835 -11025 977445 24187051 -10332652771 -466233951645 868912857645525 |
| Rev:Inv | CentralET(2 n, n) | missing | 1 -3 55 -11025 24187051 -466233951645 72359887737458035 -88047674103739207102245 |
| Rev:Inv | CentralOT(2 n + 1, n) | missing | -1 9 -835 977445 -10332652771 868912857645525 -563456403054687663235 2806102018204396870180667445 |
| Rev:Inv | ColRightT(n, n) | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Rev:Inv | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 0 -4 6 92 -2730 135284 -14034930 2918895692 -1156949125050 806123604863612 -756668870152193922 |
| Rev:Inv | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 2 8 50 572 14282 830300 108725570 30630800492 18013225703162 21717959315898452 |
| Rev:Inv | TransNat0∑ k=0..n T(n, k) k | missing | 0 1 -1 -2 24 -349 12585 -1106804 219148622 -93606371303 84167343442335 -156861056845864150 |
| Rev:Inv | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 1 -2 0 21 -345 12580 -1106798 219148615 -93606371295 84167343442326 -156861056845864140 |
| Rev:Inv | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 1 -10 56 -661 23087 -2026564 401232330 -171380368359 154098780819457 -287190927310026510 |
| Rev:Inv | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 -1 -1 15 -153 3727 -264857 46582127 -18447200377 15758979504975 -28339771840307673 |
| Rev:Inv | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 3 11 59 627 17275 1262515 222592347 88163189843 75316269568187 135443220585953139 |
| Rev:Inv | DiagRow1T(n + 1, n) | A000225 | -1 -3 -7 -15 -31 -63 -127 -255 -511 -1023 -2047 -4095 -8191 -16383 -32767 -65535 -131071 -262143 |
| Rev:Inv | DiagRow2T(n + 2, n) | A016269 | 1 9 55 285 1351 6069 26335 111645 465751 1921029 7859215 31964205 129442951 522538389 2104469695 |
| Rev:Inv | DiagRow3T(n + 3, n) | missing | -1 -45 -835 -11025 -121891 -1213065 -11291995 -100551825 -868631731 -7346524185 -61207137355 |
| Rev:Inv | DiagCol1T(n + 1, 1) | A106341 | 1 -3 9 -45 585 -21105 1858185 -367958745 157169540745 -141321010837545 263377249955934345 |
| Rev:Inv | DiagCol2T(n + 2, 2) | missing | 1 -7 55 -835 30835 -2719675 538607755 -230061795355 206863086384955 -385526761633044955 |
| Rev:Inv | DiagCol3T(n + 3, 3) | missing | 1 -15 285 -11025 977445 -193649085 82717588485 -74376706042485 138614447472278085 |
| Rev:Inv | Polysee docs | missing | 1 -1 1 1 0 1 -1 -1 1 1 1 2 -1 2 1 -1 -3 -3 1 3 1 1 4 27 -10 5 4 1 -1 -5 -355 37 -13 11 5 1 1 6 |
| Rev:Inv | PolyRow1∑ k=0..1 T(1, k) n^k | A000027 | -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 |
| Rev:Inv | PolyRow2∑ k=0..2 T(2, k) n^k | A028387 | 1 -1 -1 1 5 11 19 29 41 55 71 89 109 131 155 181 209 239 271 305 341 379 419 461 505 551 599 649 |
| Rev:Inv | PolyRow3∑ k=0..3 T(3, k) n^k | missing | -1 2 -3 -10 -13 -6 17 62 135 242 389 582 827 1130 1497 1934 2447 3042 3725 4502 5379 6362 7457 8670 |
| Rev:Inv | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 1 -1 -3 27 -355 12595 -1106819 219148643 -93606371331 84167343442371 -156861056845864195 |
| Rev:Inv | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 2 1 -10 37 -334 11377 -1000306 198091693 -84613108150 76080983338153 -141790667219471962 |
| Rev:Inv | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 0 -1 -10 -3 1424 -90305 10230366 -1915092487 416356246736 376832674245051 -2887257899812368490 |
| << | 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.