OEIS Similars: A039599, A050155
| ↕ Type | ↕ Trait | ↕ Anum | ↕ Sequence |
|---|---|---|---|
| Std | TriangleT(n, k), 0 ≤ k ≤ n | A039599 | 1 1 1 2 3 1 5 9 5 1 14 28 20 7 1 42 90 75 35 9 1 132 297 275 154 54 11 1 429 1001 1001 637 273 77 |
| Std | RevT(n, n - k), 0 ≤ k ≤ n | A050165 | 1 1 1 1 3 2 1 5 9 5 1 7 20 28 14 1 9 35 75 90 42 1 11 54 154 275 297 132 1 13 77 273 637 1001 1001 |
| Std | InvT-1(n, k), 0 ≤ k ≤ n | A085478 | 1 -1 1 1 -3 1 -1 6 -5 1 1 -10 15 -7 1 -1 15 -35 28 -9 1 1 -21 70 -84 45 -11 1 -1 28 -126 210 -165 |
| Std | RevInvT-1(n, n - k), 0 ≤ k ≤ n | A054142 | 1 1 -1 1 -3 1 1 -5 6 -1 1 -7 15 -10 1 1 -9 28 -35 15 -1 1 -11 45 -84 70 -21 1 1 -13 66 -165 210 |
| Std | Accsee docs | A050157 | 1 1 2 2 5 6 5 14 19 20 14 42 62 69 70 42 132 207 242 251 252 132 429 704 858 912 923 924 429 1430 |
| Std | AccRevsee docs | A062344 | 1 1 2 1 4 6 1 6 15 20 1 8 28 56 70 1 10 45 120 210 252 1 12 66 220 495 792 924 1 14 91 364 1001 |
| Std | AntiDiagsee docs | missing | 1 1 2 1 5 3 14 9 1 42 28 5 132 90 20 1 429 297 75 7 1430 1001 275 35 1 4862 3432 1001 154 9 16796 |
| Std | Diffx1T(n, k) (k+1) | missing | 1 1 2 2 6 3 5 18 15 4 14 56 60 28 5 42 180 225 140 45 6 132 594 825 616 270 66 7 429 2002 3003 2548 |
| Std | RowSum∑ k=0..n T(n, k) | A000984 | 1 2 6 20 70 252 924 3432 12870 48620 184756 705432 2704156 10400600 40116600 155117520 601080390 |
| Std | EvenSum∑ k=0..n T(n, k) even(k) | A001700 | 1 1 3 10 35 126 462 1716 6435 24310 92378 352716 1352078 5200300 20058300 77558760 300540195 |
| Std | OddSum∑ k=0..n T(n, k) odd(k) | A001700 | 0 1 3 10 35 126 462 1716 6435 24310 92378 352716 1352078 5200300 20058300 77558760 300540195 |
| 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) | | A000984 | 1 2 6 20 70 252 924 3432 12870 48620 184756 705432 2704156 10400600 40116600 155117520 601080390 |
| Std | DiagSum∑ k=0..n // 2 T(n - k, k) | A000958 | 1 1 3 8 24 75 243 808 2742 9458 33062 116868 417022 1500159 5434563 19808976 72596742 267343374 |
| Std | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A296771 | 1 3 13 58 257 1126 4882 20980 89497 379438 1600406 6720748 28117498 117254268 487589572 2022568168 |
| Std | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A032443 | 1 3 11 42 163 638 2510 9908 39203 155382 616666 2449868 9740686 38754732 154276028 614429672 |
| Std | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 6 45 140 3150 207900 21021 2522520 192972780 83140200 4801346550 53006865912 106340934700 |
| 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 9 28 90 297 1001 3640 13260 48450 177650 653752 2414425 8947575 33266625 124062000 463991880 |
| Std | ColMiddleT(n, n // 2) | missing | 1 1 3 9 20 75 154 637 1260 5508 10659 48279 92092 427570 807300 3817125 7152444 34295052 63882940 |
| Std | CentralET(2 n, n) | A126596 | 1 3 20 154 1260 10659 92092 807300 7152444 63882940 574221648 5188082354 47073334100 428634152730 |
| Std | CentralOT(2 n + 1, n) | missing | 1 9 75 637 5508 48279 427570 3817125 34295052 309722116 2809118403 25569834459 233460867500 |
| Std | ColLeftT(n, 0) | A000108 | 1 1 2 5 14 42 132 429 1430 4862 16796 58786 208012 742900 2674440 9694845 35357670 129644790 |
| 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) | A174687 | 1 2 9 48 275 1638 9996 62016 389367 2466750 15737865 100975680 650872404 4211628008 27341497800 |
| Std | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 0 -3 8 -5 -36 140 -176 -441 2600 -4851 -3840 47476 -119952 23400 821408 -2760545 2524176 12872519 |
| Std | TransNat0∑ k=0..n T(n, k) k | A000346 | 0 1 5 22 93 386 1586 6476 26333 106762 431910 1744436 7036530 28354132 114159428 459312152 |
| Std | TransNat1∑ k=0..n T(n, k) (k + 1) | A032443 | 1 3 11 42 163 638 2510 9908 39203 155382 616666 2449868 9740686 38754732 154276028 614429672 |
| Std | TransSqrs∑ k=0..n T(n, k) k^2 | A000531 | 0 1 7 38 187 874 3958 17548 76627 330818 1415650 6015316 25413342 106853668 447472972 1867450648 |
| Std | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A089022 | 1 3 15 87 543 3543 23823 163719 1143999 8099511 57959535 418441191 3043608351 22280372247 |
| Std | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A064062 | 1 -1 3 -13 67 -381 2307 -14589 95235 -636925 4341763 -30056445 210731011 -1493303293 10678370307 |
| Std | DiagRow1T(n + 1, n) | 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 |
| Std | DiagRow2T(n + 2, n) | A014107 | 2 9 20 35 54 77 104 135 170 209 252 299 350 405 464 527 594 665 740 819 902 989 1080 1175 1274 1377 |
| Std | DiagRow3T(n + 3, n) | missing | 5 28 75 154 273 440 663 950 1309 1748 2275 2898 3625 4464 5423 6510 7733 9100 10619 12298 14145 |
| Std | DiagCol1T(n + 1, 1) | A000245 | 1 3 9 28 90 297 1001 3432 11934 41990 149226 534888 1931540 7020405 25662825 94287120 347993910 |
| Std | DiagCol2T(n + 2, 2) | A000344 | 1 5 20 75 275 1001 3640 13260 48450 177650 653752 2414425 8947575 33266625 124062000 463991880 |
| Std | DiagCol3T(n + 3, 3) | A000588 | 1 7 35 154 637 2548 9996 38760 149226 572033 2187185 8351070 31865925 121580760 463991880 |
| Std | Polysee docs | missing | 1 1 1 2 2 1 5 6 3 1 14 20 12 4 1 42 70 51 20 5 1 132 252 222 104 30 6 1 429 924 978 548 185 42 7 1 |
| 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 | 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 |
| Std | PolyRow3∑ k=0..3 T(3, k) n^k | A062158 | 5 20 51 104 185 300 455 656 909 1220 1595 2040 2561 3164 3855 4640 5525 6516 7619 8840 10185 11660 |
| Std | PolyCol2∑ k=0..n T(n, k) 2^k | A007854 | 1 3 12 51 222 978 4338 19323 86310 386250 1730832 7763550 34847796 156503064 703149438 3160160811 |
| Std | PolyCol3∑ k=0..n T(n, k) 3^k | A076035 | 1 4 20 104 548 2904 15432 82128 437444 2331128 12426200 66250672 353258536 1883768176 10045773072 |
| Std | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 2 12 104 1150 15492 247254 4577568 96642774 2294378300 60547501696 1759037883792 55805492089516 |
| Alt | TriangleT(n, k), 0 ≤ k ≤ n | A039599 | 1 1 -1 2 -3 1 5 -9 5 -1 14 -28 20 -7 1 42 -90 75 -35 9 -1 132 -297 275 -154 54 -11 1 429 -1001 1001 |
| Alt | RevT(n, n - k), 0 ≤ k ≤ n | A050165 | 1 -1 1 1 -3 2 -1 5 -9 5 1 -7 20 -28 14 -1 9 -35 75 -90 42 1 -11 54 -154 275 -297 132 -1 13 -77 273 |
| Alt | InvT-1(n, k), 0 ≤ k ≤ n | missing | 1 -1 1 -5 3 1 11 -6 -5 1 135 -74 -55 7 1 -587 321 245 -28 -9 1 -11107 6075 4620 -532 -153 11 1 |
| Alt | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 -1 1 3 -5 1 -5 -6 11 1 7 -55 -74 135 1 -9 -28 245 321 -587 1 11 -153 -532 4620 6075 -11107 1 |
| Alt | Accsee docs | A128899 | 1 1 0 2 -1 0 5 -4 1 0 14 -14 6 -1 0 42 -48 27 -8 1 0 132 -165 110 -44 10 -1 0 429 -572 429 -208 65 |
| Alt | AccRevsee docs | missing | 1 -1 0 1 -2 0 -1 4 -5 0 1 -6 14 -14 0 -1 8 -27 48 -42 0 1 -10 44 -110 165 -132 0 -1 12 -65 208 -429 |
| Alt | AntiDiagsee docs | missing | 1 1 2 -1 5 -3 14 -9 1 42 -28 5 132 -90 20 -1 429 -297 75 -7 1430 -1001 275 -35 1 4862 -3432 1001 |
| Alt | Diffx1T(n, k) (k+1) | missing | 1 1 -2 2 -6 3 5 -18 15 -4 14 -56 60 -28 5 42 -180 225 -140 45 -6 132 -594 825 -616 270 -66 7 429 |
| 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) | A001700 | 1 1 3 10 35 126 462 1716 6435 24310 92378 352716 1352078 5200300 20058300 77558760 300540195 |
| Alt | OddSum∑ k=0..n T(n, k) odd(k) | A001700 | 0 -1 -3 -10 -35 -126 -462 -1716 -6435 -24310 -92378 -352716 -1352078 -5200300 -20058300 -77558760 |
| Alt | AltSum∑ k=0..n T(n, k) (-1)^k | A000984 | 1 2 6 20 70 252 924 3432 12870 48620 184756 705432 2704156 10400600 40116600 155117520 601080390 |
| Alt | AbsSum∑ k=0..n | T(n, k) | | A000984 | 1 2 6 20 70 252 924 3432 12870 48620 184756 705432 2704156 10400600 40116600 155117520 601080390 |
| Alt | DiagSum∑ k=0..n // 2 T(n - k, k) | A035929 | 1 1 1 2 6 19 61 200 670 2286 7918 27770 98424 351983 1268541 4602752 16799894 61642078 227239086 |
| Alt | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A000108 | 1 1 1 2 5 14 42 132 429 1430 4862 16796 58786 208012 742900 2674440 9694845 35357670 129644790 |
| Alt | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A000108 | 1 -1 -1 -2 -5 -14 -42 -132 -429 -1430 -4862 -16796 -58786 -208012 -742900 -2674440 -9694845 |
| Alt | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 6 45 140 3150 207900 21021 2522520 192972780 83140200 4801346550 53006865912 106340934700 |
| 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 9 28 90 297 1001 3640 13260 48450 177650 653752 2414425 8947575 33266625 124062000 463991880 |
| Alt | ColMiddleT(n, n // 2) | missing | 1 1 -3 -9 20 75 -154 -637 1260 5508 -10659 -48279 92092 427570 -807300 -3817125 7152444 34295052 |
| Alt | CentralET(2 n, n) | A126596 | 1 -3 20 -154 1260 -10659 92092 -807300 7152444 -63882940 574221648 -5188082354 47073334100 |
| Alt | CentralOT(2 n + 1, n) | missing | 1 -9 75 -637 5508 -48279 427570 -3817125 34295052 -309722116 2809118403 -25569834459 233460867500 |
| Alt | ColLeftT(n, 0) | A000108 | 1 1 2 5 14 42 132 429 1430 4862 16796 58786 208012 742900 2674440 9694845 35357670 129644790 |
| Alt | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 0 -3 -8 -5 36 140 176 -441 -2600 -4851 3840 47476 119952 23400 -821408 -2760545 -2524176 12872519 |
| Alt | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A174687 | 1 -2 9 -48 275 -1638 9996 -62016 389367 -2466750 15737865 -100975680 650872404 -4211628008 |
| Alt | TransNat0∑ k=0..n T(n, k) k | A000108 | 0 -1 -1 -2 -5 -14 -42 -132 -429 -1430 -4862 -16796 -58786 -208012 -742900 -2674440 -9694845 |
| Alt | TransNat1∑ k=0..n T(n, k) (k + 1) | A000108 | 1 -1 -1 -2 -5 -14 -42 -132 -429 -1430 -4862 -16796 -58786 -208012 -742900 -2674440 -9694845 |
| Alt | TransSqrs∑ k=0..n T(n, k) k^2 | A000108 | 0 -1 1 2 5 14 42 132 429 1430 4862 16796 58786 208012 742900 2674440 9694845 35357670 129644790 |
| Alt | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A064062 | 1 1 3 13 67 381 2307 14589 95235 636925 4341763 30056445 210731011 1493303293 10678370307 |
| Alt | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A089022 | 1 -3 15 -87 543 -3543 23823 -163719 1143999 -8099511 57959535 -418441191 3043608351 -22280372247 |
| Alt | DiagRow1T(n + 1, n) | 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 |
| Alt | DiagRow2T(n + 2, n) | A014107 | 2 -9 20 -35 54 -77 104 -135 170 -209 252 -299 350 -405 464 -527 594 -665 740 -819 902 -989 1080 |
| Alt | DiagRow3T(n + 3, n) | missing | 5 -28 75 -154 273 -440 663 -950 1309 -1748 2275 -2898 3625 -4464 5423 -6510 7733 -9100 10619 -12298 |
| Alt | DiagCol1T(n + 1, 1) | A000245 | -1 -3 -9 -28 -90 -297 -1001 -3432 -11934 -41990 -149226 -534888 -1931540 -7020405 -25662825 |
| Alt | DiagCol2T(n + 2, 2) | A000344 | 1 5 20 75 275 1001 3640 13260 48450 177650 653752 2414425 8947575 33266625 124062000 463991880 |
| Alt | DiagCol3T(n + 3, 3) | A000588 | -1 -7 -35 -154 -637 -2548 -9996 -38760 -149226 -572033 -2187185 -8351070 -31865925 -121580760 |
| Alt | Polysee docs | missing | 1 1 1 2 0 1 5 0 -1 1 14 0 0 -2 1 42 0 -1 2 -3 1 132 0 -2 -4 6 -4 1 429 0 -6 2 -15 12 -5 1 1430 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 | A002378 | 2 0 0 2 6 12 20 30 42 56 72 90 110 132 156 182 210 240 272 306 342 380 420 462 506 552 600 650 702 |
| Alt | PolyRow3∑ k=0..3 T(3, k) n^k | A053698 | 5 0 -1 -4 -15 -40 -85 -156 -259 -400 -585 -820 -1111 -1464 -1885 -2380 -2955 -3616 -4369 -5220 |
| Alt | PolyCol2∑ k=0..n T(n, k) 2^k | A000957 | 1 -1 0 -1 -2 -6 -18 -57 -186 -622 -2120 -7338 -25724 -91144 -325878 -1174281 -4260282 -15548694 |
| Alt | PolyCol3∑ k=0..n T(n, k) 3^k | A126984 | 1 -2 2 -4 2 -12 -12 -72 -190 -700 -2308 -8120 -28364 -100856 -360792 -1301904 -4727358 -17268636 |
| Alt | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 0 0 -4 30 -408 6090 -108792 2228310 -51665200 1337341896 -38235702360 1196772475756 |
| Rev | TriangleT(n, k), 0 ≤ k ≤ n | A050165 | 1 1 1 1 3 2 1 5 9 5 1 7 20 28 14 1 9 35 75 90 42 1 11 54 154 275 297 132 1 13 77 273 637 1001 1001 |
| Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A085478 | 1 -1 1 1 -3 1 -1 6 -5 1 1 -10 15 -7 1 -1 15 -35 28 -9 1 1 -21 70 -84 45 -11 1 -1 28 -126 210 -165 |
| Rev | Accsee docs | A062344 | 1 1 2 1 4 6 1 6 15 20 1 8 28 56 70 1 10 45 120 210 252 1 12 66 220 495 792 924 1 14 91 364 1001 |
| Rev | AccRevsee docs | A050157 | 1 1 2 2 5 6 5 14 19 20 14 42 62 69 70 42 132 207 242 251 252 132 429 704 858 912 923 924 429 1430 |
| Rev | AntiDiagsee docs | missing | 1 1 1 1 1 3 1 5 2 1 7 9 1 9 20 5 1 11 35 28 1 13 54 75 14 1 15 77 154 90 1 17 104 273 275 42 1 19 |
| Rev | Diffx1T(n, k) (k+1) | missing | 1 1 2 1 6 6 1 10 27 20 1 14 60 112 70 1 18 105 300 450 252 1 22 162 616 1375 1782 924 1 26 231 1092 |
| Rev | RowSum∑ k=0..n T(n, k) | A000984 | 1 2 6 20 70 252 924 3432 12870 48620 184756 705432 2704156 10400600 40116600 155117520 601080390 |
| Rev | EvenSum∑ k=0..n T(n, k) even(k) | A001700 | 1 1 3 10 35 126 462 1716 6435 24310 92378 352716 1352078 5200300 20058300 77558760 300540195 |
| Rev | OddSum∑ k=0..n T(n, k) odd(k) | A001700 | 0 1 3 10 35 126 462 1716 6435 24310 92378 352716 1352078 5200300 20058300 77558760 300540195 |
| 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) | | A000984 | 1 2 6 20 70 252 924 3432 12870 48620 184756 705432 2704156 10400600 40116600 155117520 601080390 |
| Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | A274115 | 1 1 2 4 8 17 35 75 157 337 712 1529 3248 6976 14869 31937 68222 146536 313487 673351 1441999 |
| Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A032443 | 1 3 11 42 163 638 2510 9908 39203 155382 616666 2449868 9740686 38754732 154276028 614429672 |
| Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A296771 | 1 3 13 58 257 1126 4882 20980 89497 379438 1600406 6720748 28117498 117254268 487589572 2022568168 |
| Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 6 45 140 3150 207900 21021 2522520 192972780 83140200 4801346550 53006865912 106340934700 |
| 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 9 28 90 297 1001 3640 13260 48450 177650 653752 2414425 8947575 33266625 124062000 463991880 |
| Rev | ColMiddleT(n, n // 2) | missing | 1 1 3 5 20 35 154 273 1260 2244 10659 19019 92092 164450 807300 1442025 7152444 12776588 63882940 |
| Rev | CentralET(2 n, n) | A126596 | 1 3 20 154 1260 10659 92092 807300 7152444 63882940 574221648 5188082354 47073334100 428634152730 |
| Rev | CentralOT(2 n + 1, n) | missing | 1 5 35 273 2244 19019 164450 1442025 12776588 114108148 1025551163 9264432775 84045912300 |
| 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) | A000108 | 1 1 2 5 14 42 132 429 1430 4862 16796 58786 208012 742900 2674440 9694845 35357670 129644790 |
| Rev | BinConv∑ k=0..n C(n, k) T(n, k) | A174687 | 1 2 9 48 275 1638 9996 62016 389367 2466750 15737865 100975680 650872404 4211628008 27341497800 |
| Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 0 -3 -8 -5 36 140 176 -441 -2600 -4851 3840 47476 119952 23400 -821408 -2760545 -2524176 12872519 |
| Rev | TransNat0∑ k=0..n T(n, k) k | A000531 | 0 1 7 38 187 874 3958 17548 76627 330818 1415650 6015316 25413342 106853668 447472972 1867450648 |
| Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | A296771 | 1 3 13 58 257 1126 4882 20980 89497 379438 1600406 6720748 28117498 117254268 487589572 2022568168 |
| Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 11 86 563 3314 18190 95052 478979 2347322 11253050 52994996 245935086 1127347636 5113862588 |
| Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A007854 | 1 3 12 51 222 978 4338 19323 86310 386250 1730832 7763550 34847796 156503064 703149438 3160160811 |
| Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A000957 | 1 -1 0 -1 -2 -6 -18 -57 -186 -622 -2120 -7338 -25724 -91144 -325878 -1174281 -4260282 -15548694 |
| Rev | DiagRow1T(n + 1, n) | A000245 | 1 3 9 28 90 297 1001 3432 11934 41990 149226 534888 1931540 7020405 25662825 94287120 347993910 |
| Rev | DiagRow2T(n + 2, n) | A000344 | 1 5 20 75 275 1001 3640 13260 48450 177650 653752 2414425 8947575 33266625 124062000 463991880 |
| Rev | DiagRow3T(n + 3, n) | A000588 | 1 7 35 154 637 2548 9996 38760 149226 572033 2187185 8351070 31865925 121580760 463991880 |
| Rev | DiagCol1T(n + 1, 1) | 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 | DiagCol2T(n + 2, 2) | A014107 | 2 9 20 35 54 77 104 135 170 209 252 299 350 405 464 527 594 665 740 819 902 989 1080 1175 1274 1377 |
| Rev | DiagCol3T(n + 3, 3) | missing | 5 28 75 154 273 440 663 950 1309 1748 2275 2898 3625 4464 5423 6510 7733 9100 10619 12298 14145 |
| Rev | Polysee docs | missing | 1 1 1 1 2 1 1 6 3 1 1 20 15 4 1 1 70 87 28 5 1 1 252 543 232 45 6 1 1 924 3543 2092 485 66 7 1 1 |
| 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 | 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 |
| Rev | PolyRow3∑ k=0..3 T(3, k) n^k | A027849 | 1 20 87 232 485 876 1435 2192 3177 4420 5951 7800 9997 12572 15555 18976 22865 27252 32167 37640 |
| Rev | PolyCol2∑ k=0..n T(n, k) 2^k | A089022 | 1 3 15 87 543 3543 23823 163719 1143999 8099511 57959535 418441191 3043608351 22280372247 |
| Rev | PolyCol3∑ k=0..n T(n, k) 3^k | A035610 | 1 4 28 232 2092 19864 195352 1970896 20275660 211823800 2240795848 23951289520 258255469816 |
| Rev | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 2 15 232 5725 197796 8859739 489517344 32231934585 2466432898300 215206959917191 |
| Inv | TriangleT(n, k), 0 ≤ k ≤ n | A085478 | 1 -1 1 1 -3 1 -1 6 -5 1 1 -10 15 -7 1 -1 15 -35 28 -9 1 1 -21 70 -84 45 -11 1 -1 28 -126 210 -165 |
| Inv | RevT(n, n - k), 0 ≤ k ≤ n | A054142 | 1 1 -1 1 -3 1 1 -5 6 -1 1 -7 15 -10 1 1 -9 28 -35 15 -1 1 -11 45 -84 70 -21 1 1 -13 66 -165 210 |
| Inv | RevInvT-1(n, n - k), 0 ≤ k ≤ n | A050165 | 1 1 1 1 3 2 1 5 9 5 1 7 20 28 14 1 9 35 75 90 42 1 11 54 154 275 297 132 1 13 77 273 637 1001 1001 |
| Inv | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | missing | 1 -1 1 -4 3 1 18 -13 -6 1 232 -168 -75 10 1 -2748 1990 887 -115 -15 1 -72268 52334 23328 -3031 -385 |
| Inv | AccRevsee docs | missing | 1 1 0 1 -2 -1 1 -4 2 1 1 -6 9 -1 0 1 -8 20 -15 0 -1 1 -10 35 -49 21 0 1 1 -12 54 -111 99 -27 1 0 1 |
| Inv | AntiDiagsee docs | A034839 | 1 -1 1 1 -1 -3 1 6 1 -1 -10 -5 1 15 15 1 -1 -21 -35 -7 1 28 70 28 1 -1 -36 -126 -84 -9 1 45 210 210 |
| Inv | Diffx1T(n, k) (k+1) | missing | 1 -1 2 1 -6 3 -1 12 -15 4 1 -20 45 -28 5 -1 30 -105 112 -45 6 1 -42 210 -336 225 -66 7 -1 56 -378 |
| Inv | EvenSum∑ k=0..n T(n, k) even(k) | A109961 | 1 -1 2 -6 17 -45 117 -305 798 -2090 5473 -14329 37513 -98209 257114 -673134 1762289 -4613733 |
| Inv | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 1 -3 7 -17 44 -116 305 -799 2091 -5473 14328 -37512 98209 -257115 673135 -1762289 4613732 |
| Inv | AltSum∑ k=0..n T(n, k) (-1)^k | A001519 | 1 -2 5 -13 34 -89 233 -610 1597 -4181 10946 -28657 75025 -196418 514229 -1346269 3524578 -9227465 |
| Inv | AbsSum∑ k=0..n | T(n, k) | | A001519 | 1 2 5 13 34 89 233 610 1597 4181 10946 28657 75025 196418 514229 1346269 3524578 9227465 24157817 |
| Inv | DiagSum∑ k=0..n // 2 T(n - k, k) | A000079 | 1 -1 2 -4 8 -16 32 -64 128 -256 512 -1024 2048 -4096 8192 -16384 32768 -65536 131072 -262144 524288 |
| Inv | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 3 30 210 1260 13860 180180 180180 6126120 116396280 116396280 2677114440 13385572200 |
| Inv | RowGcdGcd k=0..n | T(n, k) | > 1 | A000012 | 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Inv | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 3 6 15 35 84 210 495 1287 3003 8008 19448 50388 125970 319770 817190 2042975 5311735 13123110 |
| Inv | ColMiddleT(n, n // 2) | missing | 1 -1 -3 6 15 -35 -84 210 495 -1287 -3003 8008 18564 -50388 -116280 319770 735471 -2042975 -4686825 |
| Inv | CentralET(2 n, n) | A005809 | 1 -3 15 -84 495 -3003 18564 -116280 735471 -4686825 30045015 -193536720 1251677700 -8122425444 |
| Inv | CentralOT(2 n + 1, n) | A117671 | -1 6 -35 210 -1287 8008 -50388 319770 -2042975 13123110 -84672315 548354040 -3562467300 23206929840 |
| Inv | ColRightT(n, n) | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Inv | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 0 -4 3 24 -40 -145 420 784 -3948 -3024 34320 -3729 -277992 261404 2085083 -3912480 -14151072 |
| Inv | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A082759 | 1 2 8 35 160 752 3599 17446 85376 420884 2087008 10398016 52010479 261021854 1313707256 6628095035 |
| Inv | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 1 -5 3 8 -16 5 21 -33 7 40 -56 9 65 -85 11 96 -120 13 133 -161 15 176 -208 17 225 -261 19 280 |
| Inv | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A087168 | 1 -1 -1 7 -17 23 -1 -89 271 -457 287 967 -4049 8279 -8641 -7193 56143 -139657 194399 -24569 -703889 |
| Inv | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A007583 | 1 3 11 43 171 683 2731 10923 43691 174763 699051 2796203 11184811 44739243 178956971 715827883 |
| Inv | DiagRow1T(n + 1, n) | 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 |
| Inv | DiagRow2T(n + 2, n) | 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 |
| Inv | DiagRow3T(n + 3, n) | A000447 | -1 -10 -35 -84 -165 -286 -455 -680 -969 -1330 -1771 -2300 -2925 -3654 -4495 -5456 -6545 -7770 -9139 |
| Inv | DiagCol1T(n + 1, 1) | A000217 | 1 -3 6 -10 15 -21 28 -36 45 -55 66 -78 91 -105 120 -136 153 -171 190 -210 231 -253 276 -300 325 |
| Inv | DiagCol2T(n + 2, 2) | A000332 | 1 -5 15 -35 70 -126 210 -330 495 -715 1001 -1365 1820 -2380 3060 -3876 4845 -5985 7315 -8855 10626 |
| Inv | DiagCol3T(n + 3, 3) | A000579 | 1 -7 28 -84 210 -462 924 -1716 3003 -5005 8008 -12376 18564 -27132 38760 -54264 74613 -100947 |
| Inv | Polysee docs | missing | 1 -1 1 1 0 1 -1 -1 1 1 1 1 -1 2 1 -1 0 -1 1 3 1 1 -1 1 -1 5 4 1 -1 1 1 -2 7 11 5 1 1 0 -1 -1 9 29 |
| 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 | 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 |
| Inv | PolyRow3∑ k=0..3 T(3, k) n^k | missing | -1 1 -1 -1 7 29 71 139 239 377 559 791 1079 1429 1847 2339 2911 3569 4319 5167 6119 7181 8359 9659 |
| Inv | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 0 -1 -1 9 199 3691 73254 1607521 39088169 1048062951 30789776159 984771132841 34088956044012 |
| Inv:Rev | TriangleT(n, k), 0 ≤ k ≤ n | A054142 | 1 1 -1 1 -3 1 1 -5 6 -1 1 -7 15 -10 1 1 -9 28 -35 15 -1 1 -11 45 -84 70 -21 1 1 -13 66 -165 210 |
| Inv:Rev | RevT(n, n - k), 0 ≤ k ≤ n | A085478 | 1 -1 1 1 -3 1 -1 6 -5 1 1 -10 15 -7 1 -1 15 -35 28 -9 1 1 -21 70 -84 45 -11 1 -1 28 -126 210 -165 |
| Inv:Rev | InvT-1(n, k), 0 ≤ k ≤ n | missing | 1 -1 1 -4 3 1 18 -13 -6 1 232 -168 -75 10 1 -2748 1990 887 -115 -15 1 -72268 52334 23328 -3031 -385 |
| Inv:Rev | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 -1 1 3 -4 1 -6 -13 18 1 10 -75 -168 232 1 -15 -115 887 1990 -2748 1 21 -385 -3031 23328 52334 |
| Inv:Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A039599 | 1 1 1 2 3 1 5 9 5 1 14 28 20 7 1 42 90 75 35 9 1 132 297 275 154 54 11 1 429 1001 1001 637 273 77 |
| Inv:Rev | Accsee docs | missing | 1 1 0 1 -2 -1 1 -4 2 1 1 -6 9 -1 0 1 -8 20 -15 0 -1 1 -10 35 -49 21 0 1 1 -12 54 -111 99 -27 1 0 1 |
| Inv:Rev | AntiDiagsee docs | missing | 1 1 1 -1 1 -3 1 -5 1 1 -7 6 1 -9 15 -1 1 -11 28 -10 1 -13 45 -35 1 1 -15 66 -84 15 1 -17 91 -165 70 |
| Inv:Rev | EvenSum∑ k=0..n T(n, k) even(k) | A108479 | 1 1 2 7 17 44 117 305 798 2091 5473 14328 37513 98209 257114 673135 1762289 4613732 12078909 |
| Inv:Rev | OddSum∑ k=0..n T(n, k) odd(k) | A099511 | 0 -1 -3 -6 -17 -45 -116 -305 -799 -2090 -5473 -14329 -37512 -98209 -257115 -673134 -1762289 |
| Inv:Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A001519 | 1 2 5 13 34 89 233 610 1597 4181 10946 28657 75025 196418 514229 1346269 3524578 9227465 24157817 |
| Inv:Rev | AbsSum∑ k=0..n | T(n, k) | | A001519 | 1 2 5 13 34 89 233 610 1597 4181 10946 28657 75025 196418 514229 1346269 3524578 9227465 24157817 |
| Inv:Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 0 -2 -3 0 6 8 -1 -17 -21 5 48 55 -20 -135 -143 72 378 369 -244 -1054 -944 795 2927 2391 -2519 |
| Inv:Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 3 30 210 1260 13860 180180 180180 6126120 116396280 116396280 2677114440 13385572200 |
| Inv:Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | A000012 | 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Inv:Rev | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 3 6 15 35 84 210 495 1287 3003 8008 19448 50388 125970 319770 817190 2042975 5311735 13123110 |
| Inv:Rev | ColMiddleT(n, n // 2) | missing | 1 1 -3 -5 15 28 -84 -165 495 1001 -3003 -6188 18564 38760 -116280 -245157 735471 1562275 -4686825 |
| Inv:Rev | CentralET(2 n, n) | A005809 | 1 -3 15 -84 495 -3003 18564 -116280 735471 -4686825 30045015 -193536720 1251677700 -8122425444 |
| Inv:Rev | CentralOT(2 n + 1, n) | A025174 | 1 -5 28 -165 1001 -6188 38760 -245157 1562275 -10015005 64512240 -417225900 2707475148 -17620076360 |
| 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 | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 0 -4 3 24 -40 -145 420 784 -3948 -3024 34320 -3729 -277992 261404 2085083 -3912480 -14151072 |
| Inv:Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A082759 | 1 -2 8 -35 160 -752 3599 -17446 85376 -420884 2087008 -10398016 52010479 -261021854 1313707256 |
| Inv:Rev | TransNat0∑ k=0..n T(n, k) k | A138187 | 0 -1 -1 4 -3 -3 8 -5 -5 12 -7 -7 16 -9 -9 20 -11 -11 24 -13 -13 28 -15 -15 32 -17 -17 36 -19 -19 40 |
| Inv:Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 -1 1 10 -21 3 44 -65 5 102 -133 7 184 -225 9 290 -341 11 420 -481 13 574 -645 15 752 -833 17 954 |
| Inv:Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A001835 | 1 -3 11 -41 153 -571 2131 -7953 29681 -110771 413403 -1542841 5757961 -21489003 80198051 -299303201 |
| Inv:Rev | DiagRow1T(n + 1, n) | A000217 | 1 -3 6 -10 15 -21 28 -36 45 -55 66 -78 91 -105 120 -136 153 -171 190 -210 231 -253 276 -300 325 |
| Inv:Rev | DiagRow2T(n + 2, n) | A000332 | 1 -5 15 -35 70 -126 210 -330 495 -715 1001 -1365 1820 -2380 3060 -3876 4845 -5985 7315 -8855 10626 |
| Inv:Rev | DiagRow3T(n + 3, n) | A000579 | 1 -7 28 -84 210 -462 924 -1716 3003 -5005 8008 -12376 18564 -27132 38760 -54264 74613 -100947 |
| Inv:Rev | DiagCol1T(n + 1, 1) | 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 |
| Inv:Rev | DiagCol2T(n + 2, 2) | 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 |
| Inv:Rev | DiagCol3T(n + 3, 3) | A000447 | -1 -10 -35 -84 -165 -286 -455 -680 -969 -1330 -1771 -2300 -2925 -3654 -4495 -5456 -6545 -7770 -9139 |
| Inv:Rev | Polysee docs | missing | 1 1 1 1 0 1 1 -1 -1 1 1 1 -1 -2 1 1 0 7 1 -3 1 1 -1 -17 13 5 -4 1 1 1 23 -74 13 11 -5 1 1 0 -1 253 |
| 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 | 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 |
| Inv:Rev | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 1 1 7 13 13 1 -29 -83 -167 -287 -449 -659 -923 -1247 -1637 -2099 -2639 -3263 -3977 -4787 -5699 |
| Inv:Rev | PolyCol2∑ k=0..n T(n, k) 2^k | A087168 | 1 -1 -1 7 -17 23 -1 -89 271 -457 287 967 -4049 8279 -8641 -7193 56143 -139657 194399 -24569 -703889 |
| Inv:Rev | PolyCol3∑ k=0..n T(n, k) 3^k | A087169 | 1 -2 1 13 -74 253 -599 718 1801 -15467 61126 -166427 282001 87838 -2977199 14095453 -43682474 |
| Inv:Rev | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 0 -1 13 -171 2531 -42509 803706 -16922039 392603041 -9939764889 272179139629 -7994327524259 |
| << | 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.