OEIS Similars: A053121, A052173, A112554, A322378
| ↕ Type | ↕ Trait | ↕ Anum | ↕ Sequence |
|---|---|---|---|
| Std | TriangleT(n, k), 0 ≤ k ≤ n | A053121 | 1 0 1 1 0 1 0 2 0 1 2 0 3 0 1 0 5 0 4 0 1 5 0 9 0 5 0 1 0 14 0 14 0 6 0 1 14 0 28 0 20 0 7 0 1 0 42 |
| Std | RevT(n, n - k), 0 ≤ k ≤ n | A052173 | 1 1 0 1 0 1 1 0 2 0 1 0 3 0 2 1 0 4 0 5 0 1 0 5 0 9 0 5 1 0 6 0 14 0 14 0 1 0 7 0 20 0 28 0 14 1 0 |
| Std | InvT-1(n, k), 0 ≤ k ≤ n | A168561 | 1 0 1 -1 0 1 0 -2 0 1 1 0 -3 0 1 0 3 0 -4 0 1 -1 0 6 0 -5 0 1 0 -4 0 10 0 -6 0 1 1 0 -10 0 15 0 -7 |
| Std | RevInvT-1(n, n - k), 0 ≤ k ≤ n | A162515 | 1 1 0 1 0 -1 1 0 -2 0 1 0 -3 0 1 1 0 -4 0 3 0 1 0 -5 0 6 0 -1 1 0 -6 0 10 0 -4 0 1 0 -7 0 15 0 -10 |
| Std | Accsee docs | missing | 1 0 1 1 1 2 0 2 2 3 2 2 5 5 6 0 5 5 9 9 10 5 5 14 14 19 19 20 0 14 14 28 28 34 34 35 14 14 42 42 62 |
| Std | AccRevsee docs | A107430 | 1 1 1 1 1 2 1 1 3 3 1 1 4 4 6 1 1 5 5 10 10 1 1 6 6 15 15 20 1 1 7 7 21 21 35 35 1 1 8 8 28 28 56 |
| Std | AntiDiagsee docs | missing | 1 0 1 1 0 0 2 2 1 0 0 0 5 5 3 1 0 0 0 0 14 14 9 4 1 0 0 0 0 0 42 42 28 14 5 1 0 0 0 0 0 0 132 132 |
| Std | Diffx1T(n, k) (k+1) | missing | 1 0 2 1 0 3 0 4 0 4 2 0 9 0 5 0 10 0 16 0 6 5 0 27 0 25 0 7 0 28 0 56 0 36 0 8 14 0 84 0 100 0 49 0 |
| Std | RowSum∑ k=0..n T(n, k) | A001405 | 1 1 2 3 6 10 20 35 70 126 252 462 924 1716 3432 6435 12870 24310 48620 92378 184756 352716 705432 |
| Std | EvenSum∑ k=0..n T(n, k) even(k) | A126869 | 1 0 2 0 6 0 20 0 70 0 252 0 924 0 3432 0 12870 0 48620 0 184756 0 705432 0 2704156 0 10400600 0 |
| Std | OddSum∑ k=0..n T(n, k) odd(k) | A138364 | 0 1 0 3 0 10 0 35 0 126 0 462 0 1716 0 6435 0 24310 0 92378 0 352716 0 1352078 0 5200300 0 20058300 |
| Std | AltSum∑ k=0..n T(n, k) (-1)^k | A001405 | 1 -1 2 -3 6 -10 20 -35 70 -126 252 -462 924 -1716 3432 -6435 12870 -24310 48620 -92378 184756 |
| Std | AbsSum∑ k=0..n | T(n, k) | | A001405 | 1 1 2 3 6 10 20 35 70 126 252 462 924 1716 3432 6435 12870 24310 48620 92378 184756 352716 705432 |
| Std | DiagSum∑ k=0..n // 2 T(n - k, k) | A126120 | 1 0 2 0 5 0 14 0 42 0 132 0 429 0 1430 0 4862 0 16796 0 58786 0 208012 0 742900 0 2674440 0 9694845 |
| Std | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A296663 | 1 1 4 7 20 38 96 187 444 874 2000 3958 8840 17548 38528 76627 166124 330818 710256 1415650 3016056 |
| Std | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A000079 | 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576 |
| Std | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 1 2 6 20 45 42 140 3024 3150 660 207900 34320 21021 450450 2522520 13613600 192972780 4232592 |
| Std | RowGcdGcd k=0..n | T(n, k) | > 1 | A297382 | 1 1 1 2 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Std | RowMaxMax k=0..n | T(n, k) | | A101461 | 1 1 1 2 3 5 9 14 28 48 90 165 297 572 1001 2002 3640 7072 13260 25194 48450 90440 177650 326876 |
| Std | ColMiddleT(n, n // 2) | missing | 1 0 0 2 3 0 0 14 20 0 0 110 154 0 0 910 1260 0 0 7752 10659 0 0 67298 92092 0 0 592020 807300 0 0 |
| Std | CentralET(2 n, n) | A126596 | 1 0 3 0 20 0 154 0 1260 0 10659 0 92092 0 807300 0 7152444 0 63882940 0 574221648 0 5188082354 0 |
| Std | CentralOT(2 n + 1, n) | A359108 | 0 2 0 14 0 110 0 910 0 7752 0 67298 0 592020 0 5259150 0 47071640 0 423830264 0 3834669566 0 |
| Std | ColLeftT(n, 0) | A126120 | 1 0 1 0 2 0 5 0 14 0 42 0 132 0 429 0 1430 0 4862 0 16796 0 58786 0 208012 0 742900 0 2674440 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) | A344500 | 1 1 2 7 21 66 216 715 2395 8101 27598 94568 325612 1125632 3904512 13583195 47373255 165585883 |
| Std | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A344500 | 1 1 2 7 21 66 216 715 2395 8101 27598 94568 325612 1125632 3904512 13583195 47373255 165585883 |
| Std | TransNat0∑ k=0..n T(n, k) k | A045621 | 0 1 2 5 10 22 44 93 186 386 772 1586 3172 6476 12952 26333 52666 106762 213524 431910 863820 |
| Std | TransNat1∑ k=0..n T(n, k) (k + 1) | A000079 | 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576 |
| Std | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 4 11 28 66 152 339 748 1622 3496 7454 15832 33380 70192 146819 306508 637326 1323272 2738922 |
| Std | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A121724 | 1 1 5 9 45 97 485 1145 5725 14289 71445 185193 925965 2467137 12335685 33563481 167817405 464221105 |
| Std | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A121724 | 1 1 5 9 45 97 485 1145 5725 14289 71445 185193 925965 2467137 12335685 33563481 167817405 464221105 |
| Std | DiagRow2T(n + 2, n) | A000027 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 |
| Std | DiagCol1T(n + 1, 1) | A126120 | 1 0 2 0 5 0 14 0 42 0 132 0 429 0 1430 0 4862 0 16796 0 58786 0 208012 0 742900 0 2674440 0 9694845 |
| Std | DiagCol2T(n + 2, 2) | A000245 | 1 0 3 0 9 0 28 0 90 0 297 0 1001 0 3432 0 11934 0 41990 0 149226 0 534888 0 1931540 0 7020405 0 |
| Std | DiagCol3T(n + 3, 3) | A002057 | 1 0 4 0 14 0 48 0 165 0 572 0 2002 0 7072 0 25194 0 90440 0 326876 0 1188640 0 4345965 0 15967980 0 |
| Std | Polysee docs | missing | 1 0 1 1 1 1 0 2 2 1 2 3 5 3 1 0 6 12 10 4 1 5 10 30 33 17 5 1 0 20 74 110 72 26 6 1 14 35 185 366 |
| 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 | A002522 | 1 2 5 10 17 26 37 50 65 82 101 122 145 170 197 226 257 290 325 362 401 442 485 530 577 626 677 730 |
| Std | PolyRow3∑ k=0..3 T(3, k) n^k | A054602 | 0 3 12 33 72 135 228 357 528 747 1020 1353 1752 2223 2772 3405 4128 4947 5868 6897 8040 9303 10692 |
| Std | PolyCol2∑ k=0..n T(n, k) 2^k | A054341 | 1 2 5 12 30 74 185 460 1150 2868 7170 17904 44760 111834 279585 698748 1746870 4366460 10916150 |
| Std | PolyCol3∑ k=0..n T(n, k) 3^k | A126931 | 1 3 10 33 110 366 1220 4065 13550 45162 150540 501786 1672620 5575356 18584520 61948257 206494190 |
| Std | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 1 5 33 306 3650 53465 929285 18695950 427313934 10935759042 309766519722 9620876053140 |
| Alt | TriangleT(n, k), 0 ≤ k ≤ n | A053121 | 1 0 -1 1 0 1 0 -2 0 -1 2 0 3 0 1 0 -5 0 -4 0 -1 5 0 9 0 5 0 1 0 -14 0 -14 0 -6 0 -1 14 0 28 0 20 0 |
| Alt | RevT(n, n - k), 0 ≤ k ≤ n | A052173 | 1 -1 0 1 0 1 -1 0 -2 0 1 0 3 0 2 -1 0 -4 0 -5 0 1 0 5 0 9 0 5 -1 0 -6 0 -14 0 -14 0 1 0 7 0 20 0 28 |
| Alt | InvT-1(n, k), 0 ≤ k ≤ n | missing | 1 0 1 -1 0 1 0 2 0 1 1 0 -3 0 1 0 13 0 4 0 1 -1 0 6 0 -5 0 1 0 120 0 38 0 6 0 1 1 0 -10 0 15 0 -7 0 |
| Alt | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 0 1 0 -1 1 0 2 0 1 0 -3 0 1 1 0 4 0 13 0 1 0 -5 0 6 0 -1 1 0 6 0 38 0 120 0 1 0 -7 0 15 0 -10 0 |
| Alt | Accsee docs | missing | 1 0 -1 1 1 2 0 -2 -2 -3 2 2 5 5 6 0 -5 -5 -9 -9 -10 5 5 14 14 19 19 20 0 -14 -14 -28 -28 -34 -34 |
| Alt | AccRevsee docs | A107430 | 1 -1 -1 1 1 2 -1 -1 -3 -3 1 1 4 4 6 -1 -1 -5 -5 -10 -10 1 1 6 6 15 15 20 -1 -1 -7 -7 -21 -21 -35 |
| Alt | AntiDiagsee docs | missing | 1 0 1 -1 0 0 2 -2 1 0 0 0 5 -5 3 -1 0 0 0 0 14 -14 9 -4 1 0 0 0 0 0 42 -42 28 -14 5 -1 0 0 0 0 0 0 |
| Alt | Diffx1T(n, k) (k+1) | missing | 1 0 -2 1 0 3 0 -4 0 -4 2 0 9 0 5 0 -10 0 -16 0 -6 5 0 27 0 25 0 7 0 -28 0 -56 0 -36 0 -8 14 0 84 0 |
| Alt | RowSum∑ k=0..n T(n, k) | A001405 | 1 -1 2 -3 6 -10 20 -35 70 -126 252 -462 924 -1716 3432 -6435 12870 -24310 48620 -92378 184756 |
| Alt | EvenSum∑ k=0..n T(n, k) even(k) | A126869 | 1 0 2 0 6 0 20 0 70 0 252 0 924 0 3432 0 12870 0 48620 0 184756 0 705432 0 2704156 0 10400600 0 |
| Alt | OddSum∑ k=0..n T(n, k) odd(k) | A138364 | 0 -1 0 -3 0 -10 0 -35 0 -126 0 -462 0 -1716 0 -6435 0 -24310 0 -92378 0 -352716 0 -1352078 0 |
| Alt | AltSum∑ k=0..n T(n, k) (-1)^k | A001405 | 1 1 2 3 6 10 20 35 70 126 252 462 924 1716 3432 6435 12870 24310 48620 92378 184756 352716 705432 |
| Alt | AbsSum∑ k=0..n | T(n, k) | | A001405 | 1 1 2 3 6 10 20 35 70 126 252 462 924 1716 3432 6435 12870 24310 48620 92378 184756 352716 705432 |
| Alt | DiagSum∑ k=0..n // 2 T(n - k, k) | A000957 | 1 0 0 0 1 0 2 0 6 0 18 0 57 0 186 0 622 0 2120 0 7338 0 25724 0 91144 0 325878 0 1174281 0 4260282 |
| Alt | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A296663 | 1 -1 4 -7 20 -38 96 -187 444 -874 2000 -3958 8840 -17548 38528 -76627 166124 -330818 710256 |
| Alt | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A000079 | 1 -2 4 -8 16 -32 64 -128 256 -512 1024 -2048 4096 -8192 16384 -32768 65536 -131072 262144 -524288 |
| Alt | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 1 2 6 20 45 42 140 3024 3150 660 207900 34320 21021 450450 2522520 13613600 192972780 4232592 |
| Alt | RowGcdGcd k=0..n | T(n, k) | > 1 | A297382 | 1 1 1 2 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Alt | RowMaxMax k=0..n | T(n, k) | | A101461 | 1 1 1 2 3 5 9 14 28 48 90 165 297 572 1001 2002 3640 7072 13260 25194 48450 90440 177650 326876 |
| Alt | ColMiddleT(n, n // 2) | missing | 1 0 0 -2 3 0 0 -14 20 0 0 -110 154 0 0 -910 1260 0 0 -7752 10659 0 0 -67298 92092 0 0 -592020 |
| Alt | CentralET(2 n, n) | A126596 | 1 0 3 0 20 0 154 0 1260 0 10659 0 92092 0 807300 0 7152444 0 63882940 0 574221648 0 5188082354 0 |
| Alt | CentralOT(2 n + 1, n) | A359108 | 0 -2 0 -14 0 -110 0 -910 0 -7752 0 -67298 0 -592020 0 -5259150 0 -47071640 0 -423830264 0 |
| Alt | ColLeftT(n, 0) | A126120 | 1 0 1 0 2 0 5 0 14 0 42 0 132 0 429 0 1430 0 4862 0 16796 0 58786 0 208012 0 742900 0 2674440 0 |
| Alt | BinConv∑ k=0..n C(n, k) T(n, k) | A344500 | 1 -1 2 -7 21 -66 216 -715 2395 -8101 27598 -94568 325612 -1125632 3904512 -13583195 47373255 |
| Alt | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A344500 | 1 -1 2 -7 21 -66 216 -715 2395 -8101 27598 -94568 325612 -1125632 3904512 -13583195 47373255 |
| Alt | TransNat0∑ k=0..n T(n, k) k | A045621 | 0 -1 2 -5 10 -22 44 -93 186 -386 772 -1586 3172 -6476 12952 -26333 52666 -106762 213524 -431910 |
| Alt | TransNat1∑ k=0..n T(n, k) (k + 1) | A000079 | 1 -2 4 -8 16 -32 64 -128 256 -512 1024 -2048 4096 -8192 16384 -32768 65536 -131072 262144 -524288 |
| Alt | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 -1 4 -11 28 -66 152 -339 748 -1622 3496 -7454 15832 -33380 70192 -146819 306508 -637326 1323272 |
| Alt | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A121724 | 1 -1 5 -9 45 -97 485 -1145 5725 -14289 71445 -185193 925965 -2467137 12335685 -33563481 167817405 |
| Alt | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A121724 | 1 -1 5 -9 45 -97 485 -1145 5725 -14289 71445 -185193 925965 -2467137 12335685 -33563481 167817405 |
| Alt | DiagRow2T(n + 2, n) | A000027 | 1 -2 3 -4 5 -6 7 -8 9 -10 11 -12 13 -14 15 -16 17 -18 19 -20 21 -22 23 -24 25 -26 27 -28 29 -30 31 |
| Alt | DiagCol1T(n + 1, 1) | A126120 | -1 0 -2 0 -5 0 -14 0 -42 0 -132 0 -429 0 -1430 0 -4862 0 -16796 0 -58786 0 -208012 0 -742900 0 |
| Alt | DiagCol2T(n + 2, 2) | A000245 | 1 0 3 0 9 0 28 0 90 0 297 0 1001 0 3432 0 11934 0 41990 0 149226 0 534888 0 1931540 0 7020405 0 |
| Alt | DiagCol3T(n + 3, 3) | A002057 | -1 0 -4 0 -14 0 -48 0 -165 0 -572 0 -2002 0 -7072 0 -25194 0 -90440 0 -326876 0 -1188640 0 -4345965 |
| Alt | Polysee docs | missing | 1 0 1 1 -1 1 0 2 -2 1 2 -3 5 -3 1 0 6 -12 10 -4 1 5 -10 30 -33 17 -5 1 0 20 -74 110 -72 26 -6 1 14 |
| 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 | A002522 | 1 2 5 10 17 26 37 50 65 82 101 122 145 170 197 226 257 290 325 362 401 442 485 530 577 626 677 730 |
| Alt | PolyRow3∑ k=0..3 T(3, k) n^k | A054602 | 0 -3 -12 -33 -72 -135 -228 -357 -528 -747 -1020 -1353 -1752 -2223 -2772 -3405 -4128 -4947 -5868 |
| Alt | PolyCol2∑ k=0..n T(n, k) 2^k | A054341 | 1 -2 5 -12 30 -74 185 -460 1150 -2868 7170 -17904 44760 -111834 279585 -698748 1746870 -4366460 |
| Alt | PolyCol3∑ k=0..n T(n, k) 3^k | A126931 | 1 -3 10 -33 110 -366 1220 -4065 13550 -45162 150540 -501786 1672620 -5575356 18584520 -61948257 |
| Alt | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 -1 5 -33 306 -3650 53465 -929285 18695950 -427313934 10935759042 -309766519722 9620876053140 |
| Rev | TriangleT(n, k), 0 ≤ k ≤ n | A052173 | 1 1 0 1 0 1 1 0 2 0 1 0 3 0 2 1 0 4 0 5 0 1 0 5 0 9 0 5 1 0 6 0 14 0 14 0 1 0 7 0 20 0 28 0 14 1 0 |
| Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A168561 | 1 0 1 -1 0 1 0 -2 0 1 1 0 -3 0 1 0 3 0 -4 0 1 -1 0 6 0 -5 0 1 0 -4 0 10 0 -6 0 1 1 0 -10 0 15 0 -7 |
| Rev | Accsee docs | A107430 | 1 1 1 1 1 2 1 1 3 3 1 1 4 4 6 1 1 5 5 10 10 1 1 6 6 15 15 20 1 1 7 7 21 21 35 35 1 1 8 8 28 28 56 |
| Rev | AccRevsee docs | missing | 1 0 1 1 1 2 0 2 2 3 2 2 5 5 6 0 5 5 9 9 10 5 5 14 14 19 19 20 0 14 14 28 28 34 34 35 14 14 42 42 62 |
| Rev | AntiDiagsee docs | missing | 1 1 1 0 1 0 1 0 1 1 0 2 1 0 3 0 1 0 4 0 1 0 5 0 2 1 0 6 0 5 1 0 7 0 9 0 1 0 8 0 14 0 1 0 9 0 20 0 5 |
| Rev | Diffx1T(n, k) (k+1) | missing | 1 1 0 1 0 3 1 0 6 0 1 0 9 0 10 1 0 12 0 25 0 1 0 15 0 45 0 35 1 0 18 0 70 0 98 0 1 0 21 0 100 0 196 |
| Rev | RowSum∑ k=0..n T(n, k) | A001405 | 1 1 2 3 6 10 20 35 70 126 252 462 924 1716 3432 6435 12870 24310 48620 92378 184756 352716 705432 |
| Rev | EvenSum∑ k=0..n T(n, k) even(k) | A001405 | 1 1 2 3 6 10 20 35 70 126 252 462 924 1716 3432 6435 12870 24310 48620 92378 184756 352716 705432 |
| Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A001405 | 1 1 2 3 6 10 20 35 70 126 252 462 924 1716 3432 6435 12870 24310 48620 92378 184756 352716 705432 |
| Rev | AbsSum∑ k=0..n | T(n, k) | | A001405 | 1 1 2 3 6 10 20 35 70 126 252 462 924 1716 3432 6435 12870 24310 48620 92378 184756 352716 705432 |
| Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | A274112 | 1 1 1 1 2 3 4 5 8 12 17 23 35 52 75 105 157 232 337 480 712 1049 1529 2199 3248 4777 6976 10092 |
| Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A000079 | 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576 |
| Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A296663 | 1 1 4 7 20 38 96 187 444 874 2000 3958 8840 17548 38528 76627 166124 330818 710256 1415650 3016056 |
| Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 1 2 6 20 45 42 140 3024 3150 660 207900 34320 21021 450450 2522520 13613600 192972780 4232592 |
| Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | A297382 | 1 1 1 2 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Rev | RowMaxMax k=0..n | T(n, k) | | A101461 | 1 1 1 2 3 5 9 14 28 48 90 165 297 572 1001 2002 3640 7072 13260 25194 48450 90440 177650 326876 |
| Rev | ColMiddleT(n, n // 2) | missing | 1 1 0 0 3 4 0 0 20 27 0 0 154 208 0 0 1260 1700 0 0 10659 14364 0 0 92092 123970 0 0 807300 1085760 |
| Rev | CentralET(2 n, n) | A126596 | 1 0 3 0 20 0 154 0 1260 0 10659 0 92092 0 807300 0 7152444 0 63882940 0 574221648 0 5188082354 0 |
| Rev | CentralOT(2 n + 1, n) | A026005 | 1 0 4 0 27 0 208 0 1700 0 14364 0 123970 0 1085760 0 9612108 0 85795600 0 770755843 0 6960408624 0 |
| 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) | A126120 | 1 0 1 0 2 0 5 0 14 0 42 0 132 0 429 0 1430 0 4862 0 16796 0 58786 0 208012 0 742900 0 2674440 0 |
| Rev | BinConv∑ k=0..n C(n, k) T(n, k) | A344500 | 1 1 2 7 21 66 216 715 2395 8101 27598 94568 325612 1125632 3904512 13583195 47373255 165585883 |
| Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A344500 | 1 -1 2 -7 21 -66 216 -715 2395 -8101 27598 -94568 325612 -1125632 3904512 -13583195 47373255 |
| Rev | TransNat0∑ k=0..n T(n, k) k | missing | 0 0 2 4 14 28 76 152 374 748 1748 3496 7916 15832 35096 70192 153254 306508 661636 1323272 2831300 |
| Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | A296663 | 1 1 4 7 20 38 96 187 444 874 2000 3958 8840 17548 38528 76627 166124 330818 710256 1415650 3016056 |
| Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 0 4 8 44 96 344 752 2252 4880 13256 28464 72760 155008 380208 804704 1915916 4033008 9389288 |
| Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A054341 | 1 2 5 12 30 74 185 460 1150 2868 7170 17904 44760 111834 279585 698748 1746870 4366460 10916150 |
| Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A054341 | 1 -2 5 -12 30 -74 185 -460 1150 -2868 7170 -17904 44760 -111834 279585 -698748 1746870 -4366460 |
| Rev | DiagRow1T(n + 1, n) | A126120 | 1 0 2 0 5 0 14 0 42 0 132 0 429 0 1430 0 4862 0 16796 0 58786 0 208012 0 742900 0 2674440 0 9694845 |
| Rev | DiagRow2T(n + 2, n) | A000245 | 1 0 3 0 9 0 28 0 90 0 297 0 1001 0 3432 0 11934 0 41990 0 149226 0 534888 0 1931540 0 7020405 0 |
| Rev | DiagRow3T(n + 3, n) | A002057 | 1 0 4 0 14 0 48 0 165 0 572 0 2002 0 7072 0 25194 0 90440 0 326876 0 1188640 0 4345965 0 15967980 0 |
| Rev | DiagCol2T(n + 2, 2) | 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 | Polysee docs | missing | 1 1 1 1 1 1 1 2 1 1 1 3 5 1 1 1 6 9 10 1 1 1 10 45 19 17 1 1 1 20 97 190 33 26 1 1 1 35 485 442 561 |
| 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 | A002522 | 1 2 5 10 17 26 37 50 65 82 101 122 145 170 197 226 257 290 325 362 401 442 485 530 577 626 677 730 |
| Rev | PolyRow3∑ k=0..3 T(3, k) n^k | A058331 | 1 3 9 19 33 51 73 99 129 163 201 243 289 339 393 451 513 579 649 723 801 883 969 1059 1153 1251 |
| Rev | PolyCol2∑ k=0..n T(n, k) 2^k | A121724 | 1 1 5 9 45 97 485 1145 5725 14289 71445 185193 925965 2467137 12335685 33563481 167817405 464221105 |
| Rev | PolyCol3∑ k=0..n T(n, k) 3^k | A121725 | 1 1 10 19 190 442 4420 11395 113950 312814 3128140 8960878 89608780 264735892 2647358920 8006545891 |
| Rev | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 1 5 19 561 3226 245125 1680995 242303425 1833649246 429075350901 3459304779822 1195433422273585 |
| Inv | TriangleT(n, k), 0 ≤ k ≤ n | A168561 | 1 0 1 -1 0 1 0 -2 0 1 1 0 -3 0 1 0 3 0 -4 0 1 -1 0 6 0 -5 0 1 0 -4 0 10 0 -6 0 1 1 0 -10 0 15 0 -7 |
| Inv | RevT(n, n - k), 0 ≤ k ≤ n | A162515 | 1 1 0 1 0 -1 1 0 -2 0 1 0 -3 0 1 1 0 -4 0 3 0 1 0 -5 0 6 0 -1 1 0 -6 0 10 0 -4 0 1 0 -7 0 15 0 -10 |
| Inv | RevInvT-1(n, n - k), 0 ≤ k ≤ n | A052173 | 1 1 0 1 0 1 1 0 2 0 1 0 3 0 2 1 0 4 0 5 0 1 0 5 0 9 0 5 1 0 6 0 14 0 14 0 1 0 7 0 20 0 28 0 14 1 0 |
| Inv | Accsee docs | missing | 1 0 1 -1 -1 0 0 -2 -2 -1 1 1 -2 -2 -1 0 3 3 -1 -1 0 -1 -1 5 5 0 0 1 0 -4 -4 6 6 0 0 1 1 1 -9 -9 6 6 |
| Inv | AccRevsee docs | missing | 1 1 1 1 1 0 1 1 -1 -1 1 1 -2 -2 -1 1 1 -3 -3 0 0 1 1 -4 -4 2 2 1 1 1 -5 -5 5 5 1 1 1 1 -6 -6 9 9 -1 |
| Inv | AntiDiagsee docs | missing | 1 0 -1 1 0 0 1 -2 1 0 0 0 -1 3 -3 1 0 0 0 0 1 -4 6 -4 1 0 0 0 0 0 -1 5 -10 10 -5 1 0 0 0 0 0 0 1 -6 |
| Inv | Diffx1T(n, k) (k+1) | missing | 1 0 2 -1 0 3 0 -4 0 4 1 0 -9 0 5 0 6 0 -16 0 6 -1 0 18 0 -25 0 7 0 -8 0 40 0 -36 0 8 1 0 -30 0 75 0 |
| Inv | AbsSum∑ k=0..n | T(n, k) | | A000045 | 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368 75025 |
| Inv | DiagSum∑ k=0..n // 2 T(n - k, 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 |
| Inv | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 2 2 0 -3 -4 -1 4 6 2 -5 -8 -3 6 10 4 -7 -12 -5 8 14 6 -9 -16 -7 10 18 8 -11 -20 -9 12 22 10 -13 |
| Inv | RowLcmLcm k=0..n | T(n, k) | > 1 | A025560 | 1 1 1 2 3 12 30 60 210 840 1260 2520 13860 27720 180180 360360 180180 720720 6126120 12252240 |
| Inv | RowGcdGcd k=0..n | T(n, k) | > 1 | missing | 1 1 1 2 3 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Inv | RowMaxMax k=0..n | T(n, k) | | A073028 | 1 1 1 2 3 4 6 10 15 21 35 56 84 126 210 330 495 792 1287 2002 3003 5005 8008 12376 19448 31824 |
| Inv | ColMiddleT(n, n // 2) | missing | 1 0 0 -2 -3 0 0 10 15 0 0 -56 -84 0 0 330 495 0 0 -2002 -3003 0 0 12376 18564 0 0 -77520 -116280 0 |
| Inv | CentralET(2 n, n) | A005809 | 1 0 -3 0 15 0 -84 0 495 0 -3003 0 18564 0 -116280 0 735471 0 -4686825 0 30045015 0 -193536720 0 |
| Inv | CentralOT(2 n + 1, n) | A165817 | 0 -2 0 10 0 -56 0 330 0 -2002 0 12376 0 -77520 0 490314 0 -3124550 0 20030010 0 -129024480 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) | A278415 | 1 1 0 -5 -16 -24 15 197 576 724 -1200 -8832 -22801 -21293 76440 408795 922368 499104 -4446588 |
| Inv | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A278415 | 1 1 0 -5 -16 -24 15 197 576 724 -1200 -8832 -22801 -21293 76440 408795 922368 499104 -4446588 |
| Inv | TransNat0∑ k=0..n T(n, k) k | A186731 | 0 1 2 1 -2 -4 -2 3 6 3 -4 -8 -4 5 10 5 -6 -12 -6 7 14 7 -8 -16 -8 9 18 9 -10 -20 -10 11 22 11 -12 |
| Inv | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 2 2 0 -3 -4 -1 4 6 2 -5 -8 -3 6 10 4 -7 -12 -5 8 14 6 -9 -16 -7 10 18 8 -11 -20 -9 12 22 10 -13 |
| Inv | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 4 7 4 -8 -20 -15 12 39 32 -16 -64 -55 20 95 84 -24 -132 -119 28 175 160 -32 -224 -207 36 279 |
| Inv | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A106853 | 1 1 -3 -7 5 33 13 -119 -171 305 989 -231 -4187 -3263 13485 26537 -27403 -133551 -23939 510265 |
| Inv | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A106853 | 1 1 -3 -7 5 33 13 -119 -171 305 989 -231 -4187 -3263 13485 26537 -27403 -133551 -23939 510265 |
| Inv | DiagRow2T(n + 2, n) | A000027 | -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 -13 -14 -15 -16 -17 -18 -19 -20 -21 -22 -23 -24 -25 -26 -27 |
| Inv | DiagCol1T(n + 1, 1) | A142150 | 1 0 -2 0 3 0 -4 0 5 0 -6 0 7 0 -8 0 9 0 -10 0 11 0 -12 0 13 0 -14 0 15 0 -16 0 17 0 -18 0 19 0 -20 |
| Inv | DiagCol2T(n + 2, 2) | A000217 | 1 0 -3 0 6 0 -10 0 15 0 -21 0 28 0 -36 0 45 0 -55 0 66 0 -78 0 91 0 -105 0 120 0 -136 0 153 0 -171 |
| Inv | DiagCol3T(n + 3, 3) | A000292 | 1 0 -4 0 10 0 -20 0 35 0 -56 0 84 0 -120 0 165 0 -220 0 286 0 -364 0 455 0 -560 0 680 0 -816 0 969 |
| Inv | Polysee docs | missing | 1 0 1 -1 1 1 0 0 2 1 1 -1 3 3 1 0 -1 4 8 4 1 -1 0 5 21 15 5 1 0 1 6 55 56 24 6 1 1 1 7 144 209 115 |
| 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 | -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 | A242135 | 0 -1 4 21 56 115 204 329 496 711 980 1309 1704 2171 2716 3345 4064 4879 5796 6821 7960 9219 10604 |
| Inv | PolyCol2∑ k=0..n T(n, k) 2^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 |
| Inv | PolyCol3∑ k=0..n T(n, k) 3^k | A001906 | 1 3 8 21 55 144 377 987 2584 6765 17711 46368 121393 317811 832040 2178309 5702887 14930352 |
| Inv | PolyDiag∑ k=0..n T(n, k) n^k | A097690 | 1 1 3 21 209 2640 40391 726103 15003009 350382231 9127651499 262424759520 8254109243953 |
| Inv:Rev | TriangleT(n, k), 0 ≤ k ≤ n | A162515 | 1 1 0 1 0 -1 1 0 -2 0 1 0 -3 0 1 1 0 -4 0 3 0 1 0 -5 0 6 0 -1 1 0 -6 0 10 0 -4 0 1 0 -7 0 15 0 -10 |
| Inv:Rev | RevT(n, n - k), 0 ≤ k ≤ n | A168561 | 1 0 1 -1 0 1 0 -2 0 1 1 0 -3 0 1 0 3 0 -4 0 1 -1 0 6 0 -5 0 1 0 -4 0 10 0 -6 0 1 1 0 -10 0 15 0 -7 |
| Inv:Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A053121 | 1 0 1 1 0 1 0 2 0 1 2 0 3 0 1 0 5 0 4 0 1 5 0 9 0 5 0 1 0 14 0 14 0 6 0 1 14 0 28 0 20 0 7 0 1 0 42 |
| Inv:Rev | Accsee docs | missing | 1 1 1 1 1 0 1 1 -1 -1 1 1 -2 -2 -1 1 1 -3 -3 0 0 1 1 -4 -4 2 2 1 1 1 -5 -5 5 5 1 1 1 1 -6 -6 9 9 -1 |
| Inv:Rev | AccRevsee docs | missing | 1 0 1 -1 -1 0 0 -2 -2 -1 1 1 -2 -2 -1 0 3 3 -1 -1 0 -1 -1 5 5 0 0 1 0 -4 -4 6 6 0 0 1 1 1 -9 -9 6 6 |
| Inv:Rev | AntiDiagsee docs | missing | 1 1 1 0 1 0 1 0 -1 1 0 -2 1 0 -3 0 1 0 -4 0 1 0 -5 0 1 1 0 -6 0 3 1 0 -7 0 6 0 1 0 -8 0 10 0 1 0 -9 |
| Inv:Rev | Diffx1T(n, k) (k+1) | missing | 1 1 0 1 0 -3 1 0 -6 0 1 0 -9 0 5 1 0 -12 0 15 0 1 0 -15 0 30 0 -7 1 0 -18 0 50 0 -28 0 1 0 -21 0 75 |
| Inv:Rev | AbsSum∑ k=0..n | T(n, k) | | A000045 | 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368 75025 |
| Inv:Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | A099530 | 1 1 1 1 0 -1 -2 -3 -3 -2 0 3 6 8 8 5 -1 -9 -17 -22 -21 -12 5 27 48 60 55 28 -20 -80 -135 -163 -143 |
| Inv:Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 2 2 0 -3 -4 -1 4 6 2 -5 -8 -3 6 10 4 -7 -12 -5 8 14 6 -9 -16 -7 10 18 8 -11 -20 -9 12 22 10 -13 |
| Inv:Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | A025560 | 1 1 1 2 3 12 30 60 210 840 1260 2520 13860 27720 180180 360360 180180 720720 6126120 12252240 |
| Inv:Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | missing | 1 1 1 2 3 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 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) | | A073028 | 1 1 1 2 3 4 6 10 15 21 35 56 84 126 210 330 495 792 1287 2002 3003 5005 8008 12376 19448 31824 |
| Inv:Rev | ColMiddleT(n, n // 2) | missing | 1 1 0 0 -3 -4 0 0 15 21 0 0 -84 -120 0 0 495 715 0 0 -3003 -4368 0 0 18564 27132 0 0 -116280 |
| Inv:Rev | CentralET(2 n, n) | A005809 | 1 0 -3 0 15 0 -84 0 495 0 -3003 0 18564 0 -116280 0 735471 0 -4686825 0 30045015 0 -193536720 0 |
| Inv:Rev | CentralOT(2 n + 1, n) | A045721 | 1 0 -4 0 21 0 -120 0 715 0 -4368 0 27132 0 -170544 0 1081575 0 -6906900 0 44352165 0 -286097760 0 |
| 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) | A278415 | 1 1 0 -5 -16 -24 15 197 576 724 -1200 -8832 -22801 -21293 76440 408795 922368 499104 -4446588 |
| Inv:Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A278415 | 1 -1 0 5 -16 24 15 -197 576 -724 -1200 8832 -22801 21293 76440 -408795 922368 -499104 -4446588 |
| Inv:Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 0 -4 -8 4 32 40 -8 -84 -96 12 160 176 -16 -260 -280 20 384 408 -24 -532 -560 28 704 736 -32 -900 |
| Inv:Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^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 |
| Inv:Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^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 |
| Inv:Rev | DiagRow1T(n + 1, n) | A142150 | 1 0 -2 0 3 0 -4 0 5 0 -6 0 7 0 -8 0 9 0 -10 0 11 0 -12 0 13 0 -14 0 15 0 -16 0 17 0 -18 0 19 0 -20 |
| Inv:Rev | DiagRow2T(n + 2, n) | A000217 | 1 0 -3 0 6 0 -10 0 15 0 -21 0 28 0 -36 0 45 0 -55 0 66 0 -78 0 91 0 -105 0 120 0 -136 0 153 0 -171 |
| Inv:Rev | DiagRow3T(n + 3, n) | A000292 | 1 0 -4 0 10 0 -20 0 35 0 -56 0 84 0 -120 0 165 0 -220 0 286 0 -364 0 455 0 -560 0 680 0 -816 0 969 |
| Inv:Rev | DiagCol2T(n + 2, 2) | 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 |
| Inv:Rev | Polysee docs | missing | 1 1 1 1 1 1 1 0 1 1 1 -1 -3 1 1 1 -1 -7 -8 1 1 1 0 5 -17 -15 1 1 1 1 33 55 -31 -24 1 1 1 1 13 208 |
| 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 | A005563 | 1 0 -3 -8 -15 -24 -35 -48 -63 -80 -99 -120 -143 -168 -195 -224 -255 -288 -323 -360 -399 -440 -483 |
| Inv:Rev | PolyRow3∑ k=0..3 T(3, k) n^k | A056220 | 1 -1 -7 -17 -31 -49 -71 -97 -127 -161 -199 -241 -287 -337 -391 -449 -511 -577 -647 -721 -799 -881 |
| Inv:Rev | PolyCol2∑ k=0..n T(n, k) 2^k | A106853 | 1 1 -3 -7 5 33 13 -119 -171 305 989 -231 -4187 -3263 13485 26537 -27403 -133551 -23939 510265 |
| Inv:Rev | PolyCol3∑ k=0..n T(n, k) 3^k | A146078 | 1 1 -8 -17 55 208 -287 -2159 424 19855 16039 -162656 -307007 1156897 3919960 -6492113 -41771753 |
| Inv:Rev | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 1 -3 -17 209 1776 -39059 -446879 14216769 204741919 -8534720899 -148220668320 7645684627153 |
| << | 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.