OEIS Similars: A007318, A074909, A108086, A117440, A118433, A130595, A135278, A154926
| ↕ Type | ↕ Trait | ↕ Anum | ↕ Sequence |
|---|---|---|---|
| Std | TriangleT(n, k), 0 ≤ k ≤ n | A007318 | 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 |
| Std | RevT(n, n - k), 0 ≤ k ≤ n | A007318 | 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 |
| Std | InvT-1(n, k), 0 ≤ k ≤ n | A007318 | 1 -1 1 1 -2 1 -1 3 -3 1 1 -4 6 -4 1 -1 5 -10 10 -5 1 1 -6 15 -20 15 -6 1 -1 7 -21 35 -35 21 -7 1 1 |
| Std | RevInvT-1(n, n - k), 0 ≤ k ≤ n | A007318 | 1 1 -1 1 -2 1 1 -3 3 -1 1 -4 6 -4 1 1 -5 10 -10 5 -1 1 -6 15 -20 15 -6 1 1 -7 21 -35 35 -21 7 -1 1 |
| Std | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A007318 | 1 -1 1 1 -2 1 -1 3 -3 1 1 -4 6 -4 1 -1 5 -10 10 -5 1 1 -6 15 -20 15 -6 1 -1 7 -21 35 -35 21 -7 1 1 |
| Std | Accsee docs | A008949 | 1 1 2 1 3 4 1 4 7 8 1 5 11 15 16 1 6 16 26 31 32 1 7 22 42 57 63 64 1 8 29 64 99 120 127 128 1 9 37 |
| Std | AccRevsee docs | A008949 | 1 1 2 1 3 4 1 4 7 8 1 5 11 15 16 1 6 16 26 31 32 1 7 22 42 57 63 64 1 8 29 64 99 120 127 128 1 9 37 |
| Std | AntiDiagsee docs | A011973 | 1 1 1 1 1 2 1 3 1 1 4 3 1 5 6 1 1 6 10 4 1 7 15 10 1 1 8 21 20 5 1 9 28 35 15 1 1 10 36 56 35 6 1 |
| Std | Diffx1T(n, k) (k+1) | A103406 | 1 1 2 1 4 3 1 6 9 4 1 8 18 16 5 1 10 30 40 25 6 1 12 45 80 75 36 7 1 14 63 140 175 126 49 8 1 16 84 |
| Std | RowSum∑ k=0..n T(n, k) | A000079 | 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576 |
| Std | EvenSum∑ k=0..n T(n, k) even(k) | A000079 | 1 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576 |
| Std | OddSum∑ k=0..n T(n, k) odd(k) | A000079 | 0 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576 |
| 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) | | A000079 | 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576 |
| Std | DiagSum∑ k=0..n // 2 T(n - k, 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 |
| Std | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A001792 | 1 3 8 20 48 112 256 576 1280 2816 6144 13312 28672 61440 131072 278528 589824 1245184 2621440 |
| Std | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A001792 | 1 3 8 20 48 112 256 576 1280 2816 6144 13312 28672 61440 131072 278528 589824 1245184 2621440 |
| Std | RowLcmLcm k=0..n | T(n, k) | > 1 | A002944 | 1 1 2 3 12 10 60 105 280 252 2520 2310 27720 25740 24024 45045 720720 680680 12252240 11639628 |
| Std | RowGcdGcd k=0..n | T(n, k) | > 1 | A014963 | 1 1 2 3 2 5 1 7 2 3 1 11 1 13 1 1 2 17 1 19 1 1 1 23 1 5 1 3 1 29 1 31 2 1 1 1 1 37 1 1 1 41 1 43 1 |
| Std | RowMaxMax 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 | ColMiddleT(n, n // 2) | 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 | CentralET(2 n, n) | A000984 | 1 2 6 20 70 252 924 3432 12870 48620 184756 705432 2704156 10400600 40116600 155117520 601080390 |
| Std | CentralOT(2 n + 1, n) | A001700 | 1 3 10 35 126 462 1716 6435 24310 92378 352716 1352078 5200300 20058300 77558760 300540195 |
| 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) | 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) | A000984 | 1 2 6 20 70 252 924 3432 12870 48620 184756 705432 2704156 10400600 40116600 155117520 601080390 |
| Std | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^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 |
| Std | TransNat0∑ k=0..n T(n, k) k | A001787 | 0 1 4 12 32 80 192 448 1024 2304 5120 11264 24576 53248 114688 245760 524288 1114112 2359296 |
| Std | TransNat1∑ k=0..n T(n, k) (k + 1) | A001792 | 1 3 8 20 48 112 256 576 1280 2816 6144 13312 28672 61440 131072 278528 589824 1245184 2621440 |
| Std | TransSqrs∑ k=0..n T(n, k) k^2 | A001788 | 0 1 6 24 80 240 672 1792 4608 11520 28160 67584 159744 372736 860160 1966080 4456448 10027008 |
| Std | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A000244 | 1 3 9 27 81 243 729 2187 6561 19683 59049 177147 531441 1594323 4782969 14348907 43046721 129140163 |
| Std | DiagRow1T(n + 1, 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 | DiagRow2T(n + 2, n) | A000217 | 1 3 6 10 15 21 28 36 45 55 66 78 91 105 120 136 153 171 190 210 231 253 276 300 325 351 378 406 435 |
| Std | DiagRow3T(n + 3, n) | A000292 | 1 4 10 20 35 56 84 120 165 220 286 364 455 560 680 816 969 1140 1330 1540 1771 2024 2300 2600 2925 |
| Std | DiagCol1T(n + 1, 1) | 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 | DiagCol2T(n + 2, 2) | A000217 | 1 3 6 10 15 21 28 36 45 55 66 78 91 105 120 136 153 171 190 210 231 253 276 300 325 351 378 406 435 |
| Std | DiagCol3T(n + 3, 3) | A000292 | 1 4 10 20 35 56 84 120 165 220 286 364 455 560 680 816 969 1140 1330 1540 1771 2024 2300 2600 2925 |
| Std | Polysee docs | A009998 | 1 1 1 1 2 1 1 4 3 1 1 8 9 4 1 1 16 27 16 5 1 1 32 81 64 25 6 1 1 64 243 256 125 36 7 1 1 128 729 |
| 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 | A000290 | 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 784 |
| Std | PolyRow3∑ k=0..3 T(3, k) n^k | A000578 | 1 8 27 64 125 216 343 512 729 1000 1331 1728 2197 2744 3375 4096 4913 5832 6859 8000 9261 10648 |
| Std | PolyCol2∑ k=0..n T(n, k) 2^k | A000244 | 1 3 9 27 81 243 729 2187 6561 19683 59049 177147 531441 1594323 4782969 14348907 43046721 129140163 |
| Std | PolyCol3∑ k=0..n T(n, k) 3^k | A000302 | 1 4 16 64 256 1024 4096 16384 65536 262144 1048576 4194304 16777216 67108864 268435456 1073741824 |
| Std | PolyDiag∑ k=0..n T(n, k) n^k | A000169 | 1 2 9 64 625 7776 117649 2097152 43046721 1000000000 25937424601 743008370688 23298085122481 |
| Alt | TriangleT(n, k), 0 ≤ k ≤ n | A007318 | 1 1 -1 1 -2 1 1 -3 3 -1 1 -4 6 -4 1 1 -5 10 -10 5 -1 1 -6 15 -20 15 -6 1 1 -7 21 -35 35 -21 7 -1 1 |
| Alt | RevT(n, n - k), 0 ≤ k ≤ n | A007318 | 1 -1 1 1 -2 1 -1 3 -3 1 1 -4 6 -4 1 -1 5 -10 10 -5 1 1 -6 15 -20 15 -6 1 -1 7 -21 35 -35 21 -7 1 1 |
| Alt | InvT-1(n, k), 0 ≤ k ≤ n | missing | 1 -1 1 -3 2 1 5 -3 -3 1 33 -20 -18 4 1 -91 55 50 -10 -5 1 -903 546 495 -100 -45 6 1 3485 -2107 |
| Alt | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 -1 1 2 -3 1 -3 -3 5 1 4 -18 -20 33 1 -5 -10 50 55 -91 1 6 -45 -100 495 546 -903 1 -7 -21 175 |
| Alt | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A007318 | 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 |
| Alt | Accsee docs | A071919 | 1 1 0 1 -1 0 1 -2 1 0 1 -3 3 -1 0 1 -4 6 -4 1 0 1 -5 10 -10 5 -1 0 1 -6 15 -20 15 -6 1 0 1 -7 21 |
| 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) | A000079 | 1 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576 |
| Alt | OddSum∑ k=0..n T(n, k) odd(k) | A000079 | 0 -1 -2 -4 -8 -16 -32 -64 -128 -256 -512 -1024 -2048 -4096 -8192 -16384 -32768 -65536 -131072 |
| Alt | AltSum∑ k=0..n T(n, k) (-1)^k | A000079 | 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576 |
| Alt | AbsSum∑ k=0..n | T(n, k) | | A000079 | 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576 |
| Alt | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A019590 | 1 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 |
| Alt | RowLcmLcm k=0..n | T(n, k) | > 1 | A002944 | 1 1 2 3 12 10 60 105 280 252 2520 2310 27720 25740 24024 45045 720720 680680 12252240 11639628 |
| Alt | RowGcdGcd k=0..n | T(n, k) | > 1 | A014963 | 1 1 2 3 2 5 1 7 2 3 1 11 1 13 1 1 2 17 1 19 1 1 1 23 1 5 1 3 1 29 1 31 2 1 1 1 1 37 1 1 1 41 1 43 1 |
| Alt | RowMaxMax 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 | ColMiddleT(n, n // 2) | A001405 | 1 1 -2 -3 6 10 -20 -35 70 126 -252 -462 924 1716 -3432 -6435 12870 24310 -48620 -92378 184756 |
| Alt | CentralET(2 n, n) | A000984 | 1 -2 6 -20 70 -252 924 -3432 12870 -48620 184756 -705432 2704156 -10400600 40116600 -155117520 |
| Alt | CentralOT(2 n + 1, n) | A001700 | 1 -3 10 -35 126 -462 1716 -6435 24310 -92378 352716 -1352078 5200300 -20058300 77558760 -300540195 |
| 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 | BinConv∑ k=0..n C(n, k) T(n, 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 |
| Alt | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A000984 | 1 -2 6 -20 70 -252 924 -3432 12870 -48620 184756 -705432 2704156 -10400600 40116600 -155117520 |
| Alt | TransNat0∑ k=0..n T(n, k) k | A063524 | 0 -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 |
| Alt | TransSqrs∑ k=0..n T(n, k) k^2 | A039968 | 0 -1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^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 |
| Alt | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A000244 | 1 -3 9 -27 81 -243 729 -2187 6561 -19683 59049 -177147 531441 -1594323 4782969 -14348907 43046721 |
| Alt | DiagRow1T(n + 1, 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 | DiagRow2T(n + 2, 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 |
| Alt | DiagRow3T(n + 3, n) | A000292 | 1 -4 10 -20 35 -56 84 -120 165 -220 286 -364 455 -560 680 -816 969 -1140 1330 -1540 1771 -2024 2300 |
| Alt | DiagCol1T(n + 1, 1) | 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 |
| Alt | DiagCol2T(n + 2, 2) | A000217 | 1 3 6 10 15 21 28 36 45 55 66 78 91 105 120 136 153 171 190 210 231 253 276 300 325 351 378 406 435 |
| Alt | DiagCol3T(n + 3, 3) | A000292 | -1 -4 -10 -20 -35 -56 -84 -120 -165 -220 -286 -364 -455 -560 -680 -816 -969 -1140 -1330 -1540 -1771 |
| Alt | Polysee docs | missing | 1 1 1 1 0 1 1 0 -1 1 1 0 1 -2 1 1 0 -1 4 -3 1 1 0 1 -8 9 -4 1 1 0 -1 16 -27 16 -5 1 1 0 1 -32 81 |
| 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 | A000290 | 1 0 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 |
| Alt | PolyRow3∑ k=0..3 T(3, k) n^k | A000578 | 1 0 -1 -8 -27 -64 -125 -216 -343 -512 -729 -1000 -1331 -1728 -2197 -2744 -3375 -4096 -4913 -5832 |
| Alt | PolyCol3∑ k=0..n T(n, k) 3^k | A000079 | 1 -2 4 -8 16 -32 64 -128 256 -512 1024 -2048 4096 -8192 16384 -32768 65536 -131072 262144 -524288 |
| Alt | PolyDiag∑ k=0..n T(n, k) n^k | A007778 | 1 0 1 -8 81 -1024 15625 -279936 5764801 -134217728 3486784401 -100000000000 3138428376721 |
| Inv | TriangleT(n, k), 0 ≤ k ≤ n | A007318 | 1 -1 1 1 -2 1 -1 3 -3 1 1 -4 6 -4 1 -1 5 -10 10 -5 1 1 -6 15 -20 15 -6 1 -1 7 -21 35 -35 21 -7 1 1 |
| Inv | RevT(n, n - k), 0 ≤ k ≤ n | A007318 | 1 1 -1 1 -2 1 1 -3 3 -1 1 -4 6 -4 1 1 -5 10 -10 5 -1 1 -6 15 -20 15 -6 1 1 -7 21 -35 35 -21 7 -1 1 |
| Inv | RevInvT-1(n, n - k), 0 ≤ k ≤ n | A007318 | 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 |
| Inv | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | missing | 1 -1 1 -3 2 1 5 -3 -3 1 33 -20 -18 4 1 -91 55 50 -10 -5 1 -903 546 495 -100 -45 6 1 3485 -2107 |
| Inv | AccRevsee docs | A071919 | 1 1 0 1 -1 0 1 -2 1 0 1 -3 3 -1 0 1 -4 6 -4 1 0 1 -5 10 -10 5 -1 0 1 -6 15 -20 15 -6 1 0 1 -7 21 |
| Inv | AntiDiagsee docs | A011973 | 1 -1 1 1 -1 -2 1 3 1 -1 -4 -3 1 5 6 1 -1 -6 -10 -4 1 7 15 10 1 -1 -8 -21 -20 -5 1 9 28 35 15 1 -1 |
| Inv | Diffx1T(n, k) (k+1) | A103406 | 1 -1 2 1 -4 3 -1 6 -9 4 1 -8 18 -16 5 -1 10 -30 40 -25 6 1 -12 45 -80 75 -36 7 -1 14 -63 140 -175 |
| Inv | 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 |
| Inv | EvenSum∑ k=0..n T(n, k) even(k) | A000079 | 1 -1 2 -4 8 -16 32 -64 128 -256 512 -1024 2048 -4096 8192 -16384 32768 -65536 131072 -262144 524288 |
| Inv | OddSum∑ k=0..n T(n, k) odd(k) | A000079 | 0 1 -2 4 -8 16 -32 64 -128 256 -512 1024 -2048 4096 -8192 16384 -32768 65536 -131072 262144 -524288 |
| Inv | AltSum∑ k=0..n T(n, k) (-1)^k | A000079 | 1 -2 4 -8 16 -32 64 -128 256 -512 1024 -2048 4096 -8192 16384 -32768 65536 -131072 262144 -524288 |
| Inv | AbsSum∑ k=0..n | T(n, k) | | A000079 | 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576 |
| Inv | DiagSum∑ k=0..n // 2 T(n - k, 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 |
| Inv | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A019590 | 1 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 |
| Inv | RowLcmLcm k=0..n | T(n, k) | > 1 | A002944 | 1 1 2 3 12 10 60 105 280 252 2520 2310 27720 25740 24024 45045 720720 680680 12252240 11639628 |
| Inv | RowGcdGcd k=0..n | T(n, k) | > 1 | A014963 | 1 1 2 3 2 5 1 7 2 3 1 11 1 13 1 1 2 17 1 19 1 1 1 23 1 5 1 3 1 29 1 31 2 1 1 1 1 37 1 1 1 41 1 43 1 |
| Inv | RowMaxMax 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 |
| Inv | ColMiddleT(n, n // 2) | A001405 | 1 -1 -2 3 6 -10 -20 35 70 -126 -252 462 924 -1716 -3432 6435 12870 -24310 -48620 92378 184756 |
| Inv | CentralET(2 n, n) | A000984 | 1 -2 6 -20 70 -252 924 -3432 12870 -48620 184756 -705432 2704156 -10400600 40116600 -155117520 |
| Inv | CentralOT(2 n + 1, n) | A001700 | -1 3 -10 35 -126 462 -1716 6435 -24310 92378 -352716 1352078 -5200300 20058300 -77558760 300540195 |
| 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) | 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 |
| Inv | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A000984 | 1 2 6 20 70 252 924 3432 12870 48620 184756 705432 2704156 10400600 40116600 155117520 601080390 |
| Inv | TransNat0∑ k=0..n T(n, k) k | A063524 | 0 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 |
| Inv | TransNat1∑ k=0..n T(n, k) (k + 1) | A019590 | 1 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 |
| Inv | TransSqrs∑ k=0..n T(n, k) k^2 | A039968 | 0 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A000244 | 1 3 9 27 81 243 729 2187 6561 19683 59049 177147 531441 1594323 4782969 14348907 43046721 129140163 |
| Inv | DiagRow1T(n + 1, 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 | DiagRow2T(n + 2, n) | A000217 | 1 3 6 10 15 21 28 36 45 55 66 78 91 105 120 136 153 171 190 210 231 253 276 300 325 351 378 406 435 |
| Inv | DiagRow3T(n + 3, n) | A000292 | -1 -4 -10 -20 -35 -56 -84 -120 -165 -220 -286 -364 -455 -560 -680 -816 -969 -1140 -1330 -1540 -1771 |
| Inv | DiagCol1T(n + 1, 1) | 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 | DiagCol2T(n + 2, 2) | 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 | DiagCol3T(n + 3, 3) | A000292 | 1 -4 10 -20 35 -56 84 -120 165 -220 286 -364 455 -560 680 -816 969 -1140 1330 -1540 1771 -2024 2300 |
| Inv | Polysee docs | missing | 1 -1 1 1 0 1 -1 0 1 1 1 0 1 2 1 -1 0 1 4 3 1 1 0 1 8 9 4 1 -1 0 1 16 27 16 5 1 1 0 1 32 81 64 25 6 |
| 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 | A000290 | 1 0 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 |
| Inv | PolyRow3∑ k=0..3 T(3, k) n^k | A000578 | -1 0 1 8 27 64 125 216 343 512 729 1000 1331 1728 2197 2744 3375 4096 4913 5832 6859 8000 9261 |
| Inv | PolyCol2∑ k=0..n T(n, k) 2^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 | PolyCol3∑ k=0..n T(n, k) 3^k | A000079 | 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576 |
| Inv | PolyDiag∑ k=0..n T(n, k) n^k | A007778 | 1 0 1 8 81 1024 15625 279936 5764801 134217728 3486784401 100000000000 3138428376721 |
| Inv:Rev | TriangleT(n, k), 0 ≤ k ≤ n | A007318 | 1 1 -1 1 -2 1 1 -3 3 -1 1 -4 6 -4 1 1 -5 10 -10 5 -1 1 -6 15 -20 15 -6 1 1 -7 21 -35 35 -21 7 -1 1 |
| Inv:Rev | RevT(n, n - k), 0 ≤ k ≤ n | A007318 | 1 -1 1 1 -2 1 -1 3 -3 1 1 -4 6 -4 1 -1 5 -10 10 -5 1 1 -6 15 -20 15 -6 1 -1 7 -21 35 -35 21 -7 1 1 |
| Inv:Rev | InvT-1(n, k), 0 ≤ k ≤ n | missing | 1 -1 1 -3 2 1 5 -3 -3 1 33 -20 -18 4 1 -91 55 50 -10 -5 1 -903 546 495 -100 -45 6 1 3485 -2107 |
| Inv:Rev | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 -1 1 2 -3 1 -3 -3 5 1 4 -18 -20 33 1 -5 -10 50 55 -91 1 6 -45 -100 495 546 -903 1 -7 -21 175 |
| Inv:Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A007318 | 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 |
| Inv:Rev | Accsee docs | A071919 | 1 1 0 1 -1 0 1 -2 1 0 1 -3 3 -1 0 1 -4 6 -4 1 0 1 -5 10 -10 5 -1 0 1 -6 15 -20 15 -6 1 0 1 -7 21 |
| Inv:Rev | 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 |
| Inv:Rev | EvenSum∑ k=0..n T(n, k) even(k) | A000079 | 1 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576 |
| Inv:Rev | OddSum∑ k=0..n T(n, k) odd(k) | A000079 | 0 -1 -2 -4 -8 -16 -32 -64 -128 -256 -512 -1024 -2048 -4096 -8192 -16384 -32768 -65536 -131072 |
| Inv:Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A000079 | 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576 |
| Inv:Rev | AbsSum∑ k=0..n | T(n, k) | | A000079 | 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576 |
| Inv:Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A019590 | 1 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 |
| Inv:Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | A002944 | 1 1 2 3 12 10 60 105 280 252 2520 2310 27720 25740 24024 45045 720720 680680 12252240 11639628 |
| Inv:Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | A014963 | 1 1 2 3 2 5 1 7 2 3 1 11 1 13 1 1 2 17 1 19 1 1 1 23 1 5 1 3 1 29 1 31 2 1 1 1 1 37 1 1 1 41 1 43 1 |
| Inv:Rev | RowMaxMax 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 |
| Inv:Rev | ColMiddleT(n, n // 2) | A001405 | 1 1 -2 -3 6 10 -20 -35 70 126 -252 -462 924 1716 -3432 -6435 12870 24310 -48620 -92378 184756 |
| Inv:Rev | CentralET(2 n, n) | A000984 | 1 -2 6 -20 70 -252 924 -3432 12870 -48620 184756 -705432 2704156 -10400600 40116600 -155117520 |
| Inv:Rev | CentralOT(2 n + 1, n) | A001700 | 1 -3 10 -35 126 -462 1716 -6435 24310 -92378 352716 -1352078 5200300 -20058300 77558760 -300540195 |
| 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) | 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 |
| Inv:Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A000984 | 1 -2 6 -20 70 -252 924 -3432 12870 -48620 184756 -705432 2704156 -10400600 40116600 -155117520 |
| Inv:Rev | TransNat0∑ k=0..n T(n, k) k | A063524 | 0 -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 |
| Inv:Rev | TransSqrs∑ k=0..n T(n, k) k^2 | A039968 | 0 -1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^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 | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A000244 | 1 -3 9 -27 81 -243 729 -2187 6561 -19683 59049 -177147 531441 -1594323 4782969 -14348907 43046721 |
| Inv:Rev | DiagRow1T(n + 1, 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 |
| Inv:Rev | DiagRow2T(n + 2, 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 | DiagRow3T(n + 3, n) | A000292 | 1 -4 10 -20 35 -56 84 -120 165 -220 286 -364 455 -560 680 -816 969 -1140 1330 -1540 1771 -2024 2300 |
| Inv:Rev | DiagCol1T(n + 1, 1) | 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 | DiagCol2T(n + 2, 2) | A000217 | 1 3 6 10 15 21 28 36 45 55 66 78 91 105 120 136 153 171 190 210 231 253 276 300 325 351 378 406 435 |
| Inv:Rev | DiagCol3T(n + 3, 3) | A000292 | -1 -4 -10 -20 -35 -56 -84 -120 -165 -220 -286 -364 -455 -560 -680 -816 -969 -1140 -1330 -1540 -1771 |
| Inv:Rev | Polysee docs | missing | 1 1 1 1 0 1 1 0 -1 1 1 0 1 -2 1 1 0 -1 4 -3 1 1 0 1 -8 9 -4 1 1 0 -1 16 -27 16 -5 1 1 0 1 -32 81 |
| 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 | A000290 | 1 0 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 |
| Inv:Rev | PolyRow3∑ k=0..3 T(3, k) n^k | A000578 | 1 0 -1 -8 -27 -64 -125 -216 -343 -512 -729 -1000 -1331 -1728 -2197 -2744 -3375 -4096 -4913 -5832 |
| Inv:Rev | PolyCol3∑ k=0..n T(n, k) 3^k | A000079 | 1 -2 4 -8 16 -32 64 -128 256 -512 1024 -2048 4096 -8192 16384 -32768 65536 -131072 262144 -524288 |
| Inv:Rev | PolyDiag∑ k=0..n T(n, k) n^k | A007778 | 1 0 1 -8 81 -1024 15625 -279936 5764801 -134217728 3486784401 -100000000000 3138428376721 |
| << | 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.