OEIS Similars: A099174, A066325, A073278
| ↕ Type | ↕ Trait | ↕ Anum | ↕ Sequence |
|---|---|---|---|
| Std | TriangleT(n, k), 0 ≤ k ≤ n | A099174 | 1 0 1 1 0 1 0 3 0 1 3 0 6 0 1 0 15 0 10 0 1 15 0 45 0 15 0 1 0 105 0 105 0 21 0 1 105 0 420 0 210 0 |
| Std | RevT(n, n - k), 0 ≤ k ≤ n | A359760 | 1 1 0 1 0 1 1 0 3 0 1 0 6 0 3 1 0 10 0 15 0 1 0 15 0 45 0 15 1 0 21 0 105 0 105 0 1 0 28 0 210 0 |
| Std | Accsee docs | missing | 1 0 1 1 1 2 0 3 3 4 3 3 9 9 10 0 15 15 25 25 26 15 15 60 60 75 75 76 0 105 105 210 210 231 231 232 |
| Std | AccRevsee docs | missing | 1 1 1 1 1 2 1 1 4 4 1 1 7 7 10 1 1 11 11 26 26 1 1 16 16 61 61 76 1 1 22 22 127 127 232 232 1 1 29 |
| Std | AntiDiagsee docs | missing | 1 0 1 1 0 0 3 3 1 0 0 0 15 15 6 1 0 0 0 0 105 105 45 10 1 0 0 0 0 0 945 945 420 105 15 1 0 0 0 0 0 |
| Std | Diffx1T(n, k) (k+1) | missing | 1 0 2 1 0 3 0 6 0 4 3 0 18 0 5 0 30 0 40 0 6 15 0 135 0 75 0 7 0 210 0 420 0 126 0 8 105 0 1260 0 |
| Std | RowSum∑ k=0..n T(n, k) | A000085 | 1 1 2 4 10 26 76 232 764 2620 9496 35696 140152 568504 2390480 10349536 46206736 211799312 |
| Std | EvenSum∑ k=0..n T(n, k) even(k) | A066223 | 1 0 2 0 10 0 76 0 764 0 9496 0 140152 0 2390480 0 46206736 0 997313824 0 23758664096 0 618884638912 |
| Std | OddSum∑ k=0..n T(n, k) odd(k) | A066224 | 0 1 0 4 0 26 0 232 0 2620 0 35696 0 568504 0 10349536 0 211799312 0 4809701440 0 119952692896 0 |
| Std | AltSum∑ k=0..n T(n, k) (-1)^k | A000085 | 1 -1 2 -4 10 -26 76 -232 764 -2620 9496 -35696 140152 -568504 2390480 -10349536 46206736 -211799312 |
| Std | AbsSum∑ k=0..n | T(n, k) | | A000085 | 1 1 2 4 10 26 76 232 764 2620 9496 35696 140152 568504 2390480 10349536 46206736 211799312 |
| Std | DiagSum∑ k=0..n // 2 T(n - k, k) | A001515 | 1 0 2 0 7 0 37 0 266 0 2431 0 27007 0 353522 0 5329837 0 90960751 0 1733584106 0 36496226977 0 |
| Std | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 1 4 10 34 106 376 1324 5020 19324 78256 323896 1393624 6137080 27898144 129735376 619921936 |
| Std | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A000085 | 1 2 4 10 26 76 232 764 2620 9496 35696 140152 568504 2390480 10349536 46206736 211799312 997313824 |
| Std | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 1 3 6 30 45 105 420 3780 9450 103950 623700 540540 945945 14189175 113513400 1929727800 |
| Std | RowGcdGcd k=0..n | T(n, k) | > 1 | A069834 | 1 1 1 3 3 5 15 21 7 9 45 55 33 39 91 105 15 17 153 171 95 105 231 253 69 75 325 351 189 203 435 465 |
| Std | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 1 3 6 15 45 105 420 1260 4725 17325 62370 270270 945945 4729725 18918900 91891800 413513100 |
| Std | ColMiddleT(n, n // 2) | missing | 1 0 0 3 6 0 0 105 210 0 0 6930 13860 0 0 675675 1351350 0 0 87297210 174594420 0 0 14054850810 |
| Std | CentralET(2 n, n) | A359761 | 1 0 6 0 210 0 13860 0 1351350 0 174594420 0 28109701620 0 5421156741000 0 1218404977539750 0 |
| Std | CentralOT(2 n + 1, n) | missing | 0 3 0 105 0 6930 0 675675 0 87297210 0 14054850810 0 2710578370500 0 609202488769875 0 |
| Std | ColLeftT(n, 0) | A123023 | 1 0 1 0 3 0 15 0 105 0 945 0 10395 0 135135 0 2027025 0 34459425 0 654729075 0 13749310575 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) | A344501 | 1 1 2 10 40 176 916 4852 27350 163270 1009396 6504356 43400512 298682320 2118282440 15433768456 |
| Std | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A344501 | 1 1 2 10 40 176 916 4852 27350 163270 1009396 6504356 43400512 298682320 2118282440 15433768456 |
| Std | TransNat0∑ k=0..n T(n, k) k | A013989 | 0 1 2 6 16 50 156 532 1856 6876 26200 104456 428352 1821976 7959056 35857200 165592576 785514512 |
| Std | TransNat1∑ k=0..n T(n, k) (k + 1) | A000085 | 1 2 4 10 26 76 232 764 2620 9496 35696 140152 568504 2390480 10349536 46206736 211799312 997313824 |
| Std | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 4 12 40 130 456 1624 6112 23580 94960 392656 1681824 7390552 33466720 155243040 739307776 |
| Std | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A115329 | 1 1 5 13 73 281 1741 8485 57233 328753 2389141 15539261 120661465 866545993 7140942173 55667517781 |
| Std | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A115329 | 1 1 5 13 73 281 1741 8485 57233 328753 2389141 15539261 120661465 866545993 7140942173 55667517781 |
| 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 | DiagCol1T(n + 1, 1) | A123023 | 1 0 3 0 15 0 105 0 945 0 10395 0 135135 0 2027025 0 34459425 0 654729075 0 13749310575 0 |
| Std | DiagCol2T(n + 2, 2) | A001879 | 1 0 6 0 45 0 420 0 4725 0 62370 0 945945 0 16216200 0 310134825 0 6547290750 0 151242416325 0 |
| Std | DiagCol3T(n + 3, 3) | A000457 | 1 0 10 0 105 0 1260 0 17325 0 270270 0 4729725 0 91891800 0 1964187225 0 45831035250 0 |
| Std | Polysee docs | missing | 1 0 1 1 1 1 0 2 2 1 3 4 5 3 1 0 10 14 10 4 1 15 26 43 36 17 5 1 0 76 142 138 76 26 6 1 105 232 499 |
| 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 | A079908 | 0 4 14 36 76 140 234 364 536 756 1030 1364 1764 2236 2786 3420 4144 4964 5886 6916 8060 9324 10714 |
| Std | PolyCol2∑ k=0..n T(n, k) 2^k | A005425 | 1 2 5 14 43 142 499 1850 7193 29186 123109 538078 2430355 11317646 54229907 266906858 1347262321 |
| Std | PolyCol3∑ k=0..n T(n, k) 3^k | A202834 | 1 3 10 36 138 558 2364 10440 47868 227124 1112184 5607792 29057400 154465704 841143312 4685949792 |
| Std | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 1 5 36 355 4450 67731 1213240 25004393 582854940 15161973445 435430350256 13683641789115 |
| Alt | TriangleT(n, k), 0 ≤ k ≤ n | A099174 | 1 0 -1 1 0 1 0 -3 0 -1 3 0 6 0 1 0 -15 0 -10 0 -1 15 0 45 0 15 0 1 0 -105 0 -105 0 -21 0 -1 105 0 |
| Alt | RevT(n, n - k), 0 ≤ k ≤ n | A359760 | 1 -1 0 1 0 1 -1 0 -3 0 1 0 6 0 3 -1 0 -10 0 -15 0 1 0 15 0 45 0 15 -1 0 -21 0 -105 0 -105 0 1 0 28 |
| Alt | InvT-1(n, k), 0 ≤ k ≤ n | missing | 1 0 1 -1 0 1 0 3 0 1 3 0 -6 0 1 0 45 0 10 0 1 -15 0 45 0 -15 0 1 0 1365 0 315 0 21 0 1 105 0 -420 0 |
| Alt | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 0 1 0 -1 1 0 3 0 1 0 -6 0 3 1 0 10 0 45 0 1 0 -15 0 45 0 -15 1 0 21 0 315 0 1365 0 1 0 -28 0 |
| Alt | Accsee docs | missing | 1 0 -1 1 1 2 0 -3 -3 -4 3 3 9 9 10 0 -15 -15 -25 -25 -26 15 15 60 60 75 75 76 0 -105 -105 -210 -210 |
| Alt | AccRevsee docs | missing | 1 -1 -1 1 1 2 -1 -1 -4 -4 1 1 7 7 10 -1 -1 -11 -11 -26 -26 1 1 16 16 61 61 76 -1 -1 -22 -22 -127 |
| Alt | AntiDiagsee docs | missing | 1 0 1 -1 0 0 3 -3 1 0 0 0 15 -15 6 -1 0 0 0 0 105 -105 45 -10 1 0 0 0 0 0 945 -945 420 -105 15 -1 0 |
| Alt | Diffx1T(n, k) (k+1) | missing | 1 0 -2 1 0 3 0 -6 0 -4 3 0 18 0 5 0 -30 0 -40 0 -6 15 0 135 0 75 0 7 0 -210 0 -420 0 -126 0 -8 105 |
| Alt | RowSum∑ k=0..n T(n, k) | A000085 | 1 -1 2 -4 10 -26 76 -232 764 -2620 9496 -35696 140152 -568504 2390480 -10349536 46206736 -211799312 |
| Alt | EvenSum∑ k=0..n T(n, k) even(k) | A066223 | 1 0 2 0 10 0 76 0 764 0 9496 0 140152 0 2390480 0 46206736 0 997313824 0 23758664096 0 618884638912 |
| Alt | OddSum∑ k=0..n T(n, k) odd(k) | A066224 | 0 -1 0 -4 0 -26 0 -232 0 -2620 0 -35696 0 -568504 0 -10349536 0 -211799312 0 -4809701440 0 |
| Alt | AltSum∑ k=0..n T(n, k) (-1)^k | A000085 | 1 1 2 4 10 26 76 232 764 2620 9496 35696 140152 568504 2390480 10349536 46206736 211799312 |
| Alt | AbsSum∑ k=0..n | T(n, k) | | A000085 | 1 1 2 4 10 26 76 232 764 2620 9496 35696 140152 568504 2390480 10349536 46206736 211799312 |
| Alt | DiagSum∑ k=0..n // 2 T(n - k, k) | A278990 | 1 0 0 0 1 0 5 0 36 0 329 0 3655 0 47844 0 721315 0 12310199 0 234615096 0 4939227215 0 113836841041 |
| Alt | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 -1 4 -10 34 -106 376 -1324 5020 -19324 78256 -323896 1393624 -6137080 27898144 -129735376 |
| Alt | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A000085 | 1 -2 4 -10 26 -76 232 -764 2620 -9496 35696 -140152 568504 -2390480 10349536 -46206736 211799312 |
| Alt | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 1 3 6 30 45 105 420 3780 9450 103950 623700 540540 945945 14189175 113513400 1929727800 |
| Alt | RowGcdGcd k=0..n | T(n, k) | > 1 | A069834 | 1 1 1 3 3 5 15 21 7 9 45 55 33 39 91 105 15 17 153 171 95 105 231 253 69 75 325 351 189 203 435 465 |
| Alt | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 1 3 6 15 45 105 420 1260 4725 17325 62370 270270 945945 4729725 18918900 91891800 413513100 |
| Alt | ColMiddleT(n, n // 2) | missing | 1 0 0 -3 6 0 0 -105 210 0 0 -6930 13860 0 0 -675675 1351350 0 0 -87297210 174594420 0 0 |
| Alt | CentralET(2 n, n) | A359761 | 1 0 6 0 210 0 13860 0 1351350 0 174594420 0 28109701620 0 5421156741000 0 1218404977539750 0 |
| Alt | CentralOT(2 n + 1, n) | missing | 0 -3 0 -105 0 -6930 0 -675675 0 -87297210 0 -14054850810 0 -2710578370500 0 -609202488769875 0 |
| Alt | ColLeftT(n, 0) | A123023 | 1 0 1 0 3 0 15 0 105 0 945 0 10395 0 135135 0 2027025 0 34459425 0 654729075 0 13749310575 0 |
| Alt | BinConv∑ k=0..n C(n, k) T(n, k) | A344501 | 1 -1 2 -10 40 -176 916 -4852 27350 -163270 1009396 -6504356 43400512 -298682320 2118282440 |
| Alt | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A344501 | 1 -1 2 -10 40 -176 916 -4852 27350 -163270 1009396 -6504356 43400512 -298682320 2118282440 |
| Alt | TransNat0∑ k=0..n T(n, k) k | A013989 | 0 -1 2 -6 16 -50 156 -532 1856 -6876 26200 -104456 428352 -1821976 7959056 -35857200 165592576 |
| Alt | TransNat1∑ k=0..n T(n, k) (k + 1) | A000085 | 1 -2 4 -10 26 -76 232 -764 2620 -9496 35696 -140152 568504 -2390480 10349536 -46206736 211799312 |
| Alt | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 -1 4 -12 40 -130 456 -1624 6112 -23580 94960 -392656 1681824 -7390552 33466720 -155243040 |
| Alt | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A115329 | 1 -1 5 -13 73 -281 1741 -8485 57233 -328753 2389141 -15539261 120661465 -866545993 7140942173 |
| Alt | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A115329 | 1 -1 5 -13 73 -281 1741 -8485 57233 -328753 2389141 -15539261 120661465 -866545993 7140942173 |
| 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 | DiagCol1T(n + 1, 1) | A123023 | -1 0 -3 0 -15 0 -105 0 -945 0 -10395 0 -135135 0 -2027025 0 -34459425 0 -654729075 0 -13749310575 0 |
| Alt | DiagCol2T(n + 2, 2) | A001879 | 1 0 6 0 45 0 420 0 4725 0 62370 0 945945 0 16216200 0 310134825 0 6547290750 0 151242416325 0 |
| Alt | DiagCol3T(n + 3, 3) | A000457 | -1 0 -10 0 -105 0 -1260 0 -17325 0 -270270 0 -4729725 0 -91891800 0 -1964187225 0 -45831035250 0 |
| Alt | Polysee docs | missing | 1 0 1 1 -1 1 0 2 -2 1 3 -4 5 -3 1 0 10 -14 10 -4 1 15 -26 43 -36 17 -5 1 0 76 -142 138 -76 26 -6 1 |
| 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 | A079908 | 0 -4 -14 -36 -76 -140 -234 -364 -536 -756 -1030 -1364 -1764 -2236 -2786 -3420 -4144 -4964 -5886 |
| Alt | PolyCol2∑ k=0..n T(n, k) 2^k | A005425 | 1 -2 5 -14 43 -142 499 -1850 7193 -29186 123109 -538078 2430355 -11317646 54229907 -266906858 |
| Alt | PolyCol3∑ k=0..n T(n, k) 3^k | A202834 | 1 -3 10 -36 138 -558 2364 -10440 47868 -227124 1112184 -5607792 29057400 -154465704 841143312 |
| Alt | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 -1 5 -36 355 -4450 67731 -1213240 25004393 -582854940 15161973445 -435430350256 13683641789115 |
| Rev | TriangleT(n, k), 0 ≤ k ≤ n | A359760 | 1 1 0 1 0 1 1 0 3 0 1 0 6 0 3 1 0 10 0 15 0 1 0 15 0 45 0 15 1 0 21 0 105 0 105 0 1 0 28 0 210 0 |
| Rev | Accsee docs | missing | 1 1 1 1 1 2 1 1 4 4 1 1 7 7 10 1 1 11 11 26 26 1 1 16 16 61 61 76 1 1 22 22 127 127 232 232 1 1 29 |
| Rev | AccRevsee docs | missing | 1 0 1 1 1 2 0 3 3 4 3 3 9 9 10 0 15 15 25 25 26 15 15 60 60 75 75 76 0 105 105 210 210 231 231 232 |
| Rev | AntiDiagsee docs | missing | 1 1 1 0 1 0 1 0 1 1 0 3 1 0 6 0 1 0 10 0 1 0 15 0 3 1 0 21 0 15 1 0 28 0 45 0 1 0 36 0 105 0 1 0 45 |
| Rev | Diffx1T(n, k) (k+1) | missing | 1 1 0 1 0 3 1 0 9 0 1 0 18 0 15 1 0 30 0 75 0 1 0 45 0 225 0 105 1 0 63 0 525 0 735 0 1 0 84 0 1050 |
| Rev | RowSum∑ k=0..n T(n, k) | A000085 | 1 1 2 4 10 26 76 232 764 2620 9496 35696 140152 568504 2390480 10349536 46206736 211799312 |
| Rev | EvenSum∑ k=0..n T(n, k) even(k) | A000085 | 1 1 2 4 10 26 76 232 764 2620 9496 35696 140152 568504 2390480 10349536 46206736 211799312 |
| Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A000085 | 1 1 2 4 10 26 76 232 764 2620 9496 35696 140152 568504 2390480 10349536 46206736 211799312 |
| Rev | AbsSum∑ k=0..n | T(n, k) | | A000085 | 1 1 2 4 10 26 76 232 764 2620 9496 35696 140152 568504 2390480 10349536 46206736 211799312 |
| Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 1 1 2 4 7 11 19 37 74 142 271 539 1117 2329 4832 10126 21709 47297 103579 227917 507176 1143424 |
| Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A000085 | 1 2 4 10 26 76 232 764 2620 9496 35696 140152 568504 2390480 10349536 46206736 211799312 997313824 |
| Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 1 4 10 34 106 376 1324 5020 19324 78256 323896 1393624 6137080 27898144 129735376 619921936 |
| Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 1 3 6 30 45 105 420 3780 9450 103950 623700 540540 945945 14189175 113513400 1929727800 |
| Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | A069834 | 1 1 1 3 3 5 15 21 7 9 45 55 33 39 91 105 15 17 153 171 95 105 231 253 69 75 325 351 189 203 435 465 |
| Rev | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 1 3 6 15 45 105 420 1260 4725 17325 62370 270270 945945 4729725 18918900 91891800 413513100 |
| Rev | ColMiddleT(n, n // 2) | missing | 1 1 0 0 6 10 0 0 210 378 0 0 13860 25740 0 0 1351350 2552550 0 0 174594420 333316620 0 0 |
| Rev | CentralET(2 n, n) | A359761 | 1 0 6 0 210 0 13860 0 1351350 0 174594420 0 28109701620 0 5421156741000 0 1218404977539750 0 |
| Rev | CentralOT(2 n + 1, n) | missing | 1 0 10 0 378 0 25740 0 2552550 0 333316620 0 54057118500 0 10480903032600 0 2365139074047750 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) | A123023 | 1 0 1 0 3 0 15 0 105 0 945 0 10395 0 135135 0 2027025 0 34459425 0 654729075 0 13749310575 0 |
| Rev | BinConv∑ k=0..n C(n, k) T(n, k) | A344501 | 1 1 2 10 40 176 916 4852 27350 163270 1009396 6504356 43400512 298682320 2118282440 15433768456 |
| Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A344501 | 1 -1 2 -10 40 -176 916 -4852 27350 -163270 1009396 -6504356 43400512 -298682320 2118282440 |
| Rev | TransNat0∑ k=0..n T(n, k) k | missing | 0 0 2 6 24 80 300 1092 4256 16704 68760 288200 1253472 5568576 25507664 119385840 573715200 |
| Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 1 4 10 34 106 376 1324 5020 19324 78256 323896 1393624 6137080 27898144 129735376 619921936 |
| Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 0 4 12 72 280 1320 5544 25312 112032 520560 2413840 11583264 56096352 279147232 1408172640 |
| Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A005425 | 1 2 5 14 43 142 499 1850 7193 29186 123109 538078 2430355 11317646 54229907 266906858 1347262321 |
| Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A005425 | 1 -2 5 -14 43 -142 499 -1850 7193 -29186 123109 -538078 2430355 -11317646 54229907 -266906858 |
| Rev | DiagRow1T(n + 1, n) | A123023 | 1 0 3 0 15 0 105 0 945 0 10395 0 135135 0 2027025 0 34459425 0 654729075 0 13749310575 0 |
| Rev | DiagRow2T(n + 2, n) | A001879 | 1 0 6 0 45 0 420 0 4725 0 62370 0 945945 0 16216200 0 310134825 0 6547290750 0 151242416325 0 |
| Rev | DiagRow3T(n + 3, n) | A000457 | 1 0 10 0 105 0 1260 0 17325 0 270270 0 4729725 0 91891800 0 1964187225 0 45831035250 0 |
| 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 |
| Rev | Polysee docs | missing | 1 1 1 1 1 1 1 2 1 1 1 4 5 1 1 1 10 13 10 1 1 1 26 73 28 17 1 1 1 76 281 298 49 26 1 1 1 232 1741 |
| 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 | A056107 | 1 4 13 28 49 76 109 148 193 244 301 364 433 508 589 676 769 868 973 1084 1201 1324 1453 1588 1729 |
| Rev | PolyCol2∑ k=0..n T(n, k) 2^k | A115329 | 1 1 5 13 73 281 1741 8485 57233 328753 2389141 15539261 120661465 866545993 7140942173 55667517781 |
| Rev | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 1 10 28 298 1306 14716 85240 1012348 7149628 89149816 732616336 9558448120 88681012408 |
| Rev | PolyDiag∑ k=0..n T(n, k) n^k | A359739 | 1 1 5 28 865 9626 758701 12606280 1872570113 41351249980 9925656304501 273345587759696 |
| Inv | RevInvT-1(n, n - k), 0 ≤ k ≤ n | A359760 | 1 1 0 1 0 1 1 0 3 0 1 0 6 0 3 1 0 10 0 15 0 1 0 15 0 45 0 15 1 0 21 0 105 0 105 0 1 0 28 0 210 0 |
| Inv | Accsee docs | missing | 1 0 1 -1 -1 0 0 -3 -3 -2 3 3 -3 -3 -2 0 15 15 5 5 6 -15 -15 30 30 15 15 16 0 -105 -105 0 0 -21 -21 |
| Inv | AccRevsee docs | missing | 1 1 1 1 1 0 1 1 -2 -2 1 1 -5 -5 -2 1 1 -9 -9 6 6 1 1 -14 -14 31 31 16 1 1 -20 -20 85 85 -20 -20 1 1 |
| Inv | AntiDiagsee docs | missing | 1 0 -1 1 0 0 3 -3 1 0 0 0 -15 15 -6 1 0 0 0 0 105 -105 45 -10 1 0 0 0 0 0 -945 945 -420 105 -15 1 0 |
| Inv | Diffx1T(n, k) (k+1) | missing | 1 0 2 -1 0 3 0 -6 0 4 3 0 -18 0 5 0 30 0 -40 0 6 -15 0 135 0 -75 0 7 0 -210 0 420 0 -126 0 8 105 0 |
| Inv | RowSum∑ k=0..n T(n, k) | A001464 | 1 1 0 -2 -2 6 16 -20 -132 28 1216 936 -12440 -23672 138048 469456 -1601264 -9112560 18108928 |
| Inv | EvenSum∑ k=0..n T(n, k) even(k) | A362718 | 1 0 0 0 -2 0 16 0 -132 0 1216 0 -12440 0 138048 0 -1601264 0 18108928 0 -161934624 0 -404007680 0 |
| Inv | OddSum∑ k=0..n T(n, k) odd(k) | A131441 | 0 1 0 -2 0 6 0 -20 0 28 0 936 0 -23672 0 469456 0 -9112560 0 182135008 0 -3804634784 0 83297957568 |
| Inv | AltSum∑ k=0..n T(n, k) (-1)^k | A001464 | 1 -1 0 2 -2 -6 16 20 -132 -28 1216 -936 -12440 23672 138048 -469456 -1601264 9112560 18108928 |
| Inv | AbsSum∑ k=0..n | T(n, k) | | A000085 | 1 1 2 4 10 26 76 232 764 2620 9496 35696 140152 568504 2390480 10349536 46206736 211799312 |
| Inv | DiagSum∑ k=0..n // 2 T(n - k, k) | A278990 | 1 0 0 0 1 0 -5 0 36 0 -329 0 3655 0 -47844 0 721315 0 -12310199 0 234615096 0 -4939227215 0 |
| Inv | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 1 -2 -8 -2 46 76 -272 -1028 1468 13096 -2144 -172952 -169688 2402128 5440576 -34732784 -136804592 |
| Inv | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 2 2 -2 -10 -4 52 92 -292 -1160 1496 14312 -1208 -185392 -193360 2540176 5910032 -36334048 |
| Inv | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 1 3 6 30 45 105 420 3780 9450 103950 623700 540540 945945 14189175 113513400 1929727800 |
| Inv | RowGcdGcd k=0..n | T(n, k) | > 1 | A069834 | 1 1 1 3 3 5 15 21 7 9 45 55 33 39 91 105 15 17 153 171 95 105 231 253 69 75 325 351 189 203 435 465 |
| Inv | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 1 3 6 15 45 105 420 1260 4725 17325 62370 270270 945945 4729725 18918900 91891800 413513100 |
| Inv | ColMiddleT(n, n // 2) | missing | 1 0 0 -3 -6 0 0 105 210 0 0 -6930 -13860 0 0 675675 1351350 0 0 -87297210 -174594420 0 0 |
| Inv | CentralET(2 n, n) | A359761 | 1 0 -6 0 210 0 -13860 0 1351350 0 -174594420 0 28109701620 0 -5421156741000 0 1218404977539750 0 |
| Inv | CentralOT(2 n + 1, n) | missing | 0 -3 0 105 0 -6930 0 675675 0 -87297210 0 14054850810 0 -2710578370500 0 609202488769875 0 |
| Inv | ColLeftT(n, 0) | A123023 | 1 0 -1 0 3 0 -15 0 105 0 -945 0 10395 0 -135135 0 2027025 0 -34459425 0 654729075 0 -13749310575 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) | missing | 1 1 0 -8 -32 -24 436 2500 2262 -51002 -319544 -133704 9545680 55736032 -46326552 -2422602104 |
| Inv | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 1 0 -8 -32 -24 436 2500 2262 -51002 -319544 -133704 9545680 55736032 -46326552 -2422602104 |
| Inv | TransNat0∑ k=0..n T(n, k) k | missing | 0 1 2 0 -8 -10 36 112 -160 -1188 280 13376 11232 -161720 -331408 2070720 7511296 -27221488 |
| Inv | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 2 2 -2 -10 -4 52 92 -292 -1160 1496 14312 -1208 -185392 -193360 2540176 5910032 -36334048 |
| Inv | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 4 6 -8 -50 -24 364 736 -2628 -11600 16456 171744 -15704 -2595488 -2900400 40642816 100470544 |
| Inv | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A362176 | 1 1 -3 -11 25 201 -299 -5123 3249 167185 50221 -6637179 -8846903 309737689 769776645 -16575533939 |
| Inv | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A362176 | 1 1 -3 -11 25 201 -299 -5123 3249 167185 50221 -6637179 -8846903 309737689 769776645 -16575533939 |
| 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 |
| Inv | DiagCol1T(n + 1, 1) | A123023 | 1 0 -3 0 15 0 -105 0 945 0 -10395 0 135135 0 -2027025 0 34459425 0 -654729075 0 13749310575 0 |
| Inv | DiagCol2T(n + 2, 2) | A001879 | 1 0 -6 0 45 0 -420 0 4725 0 -62370 0 945945 0 -16216200 0 310134825 0 -6547290750 0 151242416325 0 |
| Inv | DiagCol3T(n + 3, 3) | A000457 | 1 0 -10 0 105 0 -1260 0 17325 0 -270270 0 4729725 0 -91891800 0 1964187225 0 -45831035250 0 |
| Inv | Polysee docs | missing | 1 0 1 -1 1 1 0 0 2 1 3 -2 3 3 1 0 -2 2 8 4 1 -15 6 -5 18 15 5 1 0 16 -18 30 52 24 6 1 105 -20 -11 |
| 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 | A058794 | 0 -2 2 18 52 110 198 322 488 702 970 1298 1692 2158 2702 3330 4048 4862 5778 6802 7940 9198 10582 |
| Inv | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 2 3 2 -5 -18 -11 86 249 -190 -2621 -3342 22147 84398 -119115 -1419802 -1052879 20611074 59121091 |
| Inv | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 3 8 18 30 18 -96 -396 -516 1620 9504 12312 -67608 -350568 -172800 4389552 15760656 -22950864 |
| Inv | PolyDiag∑ k=0..n T(n, k) n^k | A089466 | 1 1 3 18 163 1950 28821 505876 10270569 236644092 6098971555 173823708696 5427760272507 |
| Inv:Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A099174 | 1 0 1 1 0 1 0 3 0 1 3 0 6 0 1 0 15 0 10 0 1 15 0 45 0 15 0 1 0 105 0 105 0 21 0 1 105 0 420 0 210 0 |
| Inv:Rev | Accsee docs | missing | 1 1 1 1 1 0 1 1 -2 -2 1 1 -5 -5 -2 1 1 -9 -9 6 6 1 1 -14 -14 31 31 16 1 1 -20 -20 85 85 -20 -20 1 1 |
| Inv:Rev | AccRevsee docs | missing | 1 0 1 -1 -1 0 0 -3 -3 -2 3 3 -3 -3 -2 0 15 15 5 5 6 -15 -15 30 30 15 15 16 0 -105 -105 0 0 -21 -21 |
| Inv:Rev | AntiDiagsee docs | missing | 1 1 1 0 1 0 1 0 -1 1 0 -3 1 0 -6 0 1 0 -10 0 1 0 -15 0 3 1 0 -21 0 15 1 0 -28 0 45 0 1 0 -36 0 105 |
| Inv:Rev | Diffx1T(n, k) (k+1) | missing | 1 1 0 1 0 -3 1 0 -9 0 1 0 -18 0 15 1 0 -30 0 75 0 1 0 -45 0 225 0 -105 1 0 -63 0 525 0 -735 0 1 0 |
| Inv:Rev | RowSum∑ k=0..n T(n, k) | A001464 | 1 1 0 -2 -2 6 16 -20 -132 28 1216 936 -12440 -23672 138048 469456 -1601264 -9112560 18108928 |
| Inv:Rev | EvenSum∑ k=0..n T(n, k) even(k) | A001464 | 1 1 0 -2 -2 6 16 -20 -132 28 1216 936 -12440 -23672 138048 469456 -1601264 -9112560 18108928 |
| Inv:Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A001464 | 1 1 0 -2 -2 6 16 -20 -132 28 1216 936 -12440 -23672 138048 469456 -1601264 -9112560 18108928 |
| Inv:Rev | AbsSum∑ k=0..n | T(n, k) | | A000085 | 1 1 2 4 10 26 76 232 764 2620 9496 35696 140152 568504 2390480 10349536 46206736 211799312 |
| Inv:Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 1 1 0 -2 -5 -9 -11 -5 18 70 151 219 145 -347 -1650 -3944 -6251 -4455 11293 56635 141816 231184 |
| Inv:Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 2 2 -2 -10 -4 52 92 -292 -1160 1496 14312 -1208 -185392 -193360 2540176 5910032 -36334048 |
| Inv:Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 1 -2 -8 -2 46 76 -272 -1028 1468 13096 -2144 -172952 -169688 2402128 5440576 -34732784 -136804592 |
| Inv:Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 1 3 6 30 45 105 420 3780 9450 103950 623700 540540 945945 14189175 113513400 1929727800 |
| Inv:Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | A069834 | 1 1 1 3 3 5 15 21 7 9 45 55 33 39 91 105 15 17 153 171 95 105 231 253 69 75 325 351 189 203 435 465 |
| Inv:Rev | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 1 3 6 15 45 105 420 1260 4725 17325 62370 270270 945945 4729725 18918900 91891800 413513100 |
| Inv:Rev | ColMiddleT(n, n // 2) | missing | 1 1 0 0 -6 -10 0 0 210 378 0 0 -13860 -25740 0 0 1351350 2552550 0 0 -174594420 -333316620 0 0 |
| Inv:Rev | CentralET(2 n, n) | A359761 | 1 0 -6 0 210 0 -13860 0 1351350 0 -174594420 0 28109701620 0 -5421156741000 0 1218404977539750 0 |
| Inv:Rev | CentralOT(2 n + 1, n) | missing | 1 0 -10 0 378 0 -25740 0 2552550 0 -333316620 0 54057118500 0 -10480903032600 0 2365139074047750 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 | ColRightT(n, n) | A123023 | 1 0 -1 0 3 0 -15 0 105 0 -945 0 10395 0 -135135 0 2027025 0 -34459425 0 654729075 0 -13749310575 0 |
| Inv:Rev | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 1 0 -8 -32 -24 436 2500 2262 -51002 -319544 -133704 9545680 55736032 -46326552 -2422602104 |
| Inv:Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -1 0 8 -32 24 436 -2500 2262 51002 -319544 133704 9545680 -55736032 -46326552 2422602104 |
| Inv:Rev | TransNat0∑ k=0..n T(n, k) k | missing | 0 0 -2 -6 0 40 60 -252 -896 1440 11880 -3080 -160512 -146016 2264080 4971120 -33131520 -127692032 |
| Inv:Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 1 -2 -8 -2 46 76 -272 -1028 1468 13096 -2144 -172952 -169688 2402128 5440576 -34732784 -136804592 |
| Inv:Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 0 -4 -12 24 200 120 -2184 -5152 21024 104400 -164560 -1889184 188448 33741344 40605600 -609642240 |
| Inv:Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 2 3 2 -5 -18 -11 86 249 -190 -2621 -3342 22147 84398 -119115 -1419802 -1052879 20611074 59121091 |
| Inv:Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 -2 3 -2 -5 18 -11 -86 249 190 -2621 3342 22147 -84398 -119115 1419802 -1052879 -20611074 59121091 |
| Inv:Rev | DiagRow1T(n + 1, n) | A123023 | 1 0 -3 0 15 0 -105 0 945 0 -10395 0 135135 0 -2027025 0 34459425 0 -654729075 0 13749310575 0 |
| Inv:Rev | DiagRow2T(n + 2, n) | A001879 | 1 0 -6 0 45 0 -420 0 4725 0 -62370 0 945945 0 -16216200 0 310134825 0 -6547290750 0 151242416325 0 |
| Inv:Rev | DiagRow3T(n + 3, n) | A000457 | 1 0 -10 0 105 0 -1260 0 17325 0 -270270 0 4729725 0 -91891800 0 1964187225 0 -45831035250 0 |
| 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 |
| Inv:Rev | Polysee docs | missing | 1 1 1 1 1 1 1 0 1 1 1 -2 -3 1 1 1 -2 -11 -8 1 1 1 6 25 -26 -15 1 1 1 16 201 190 -47 -24 1 1 1 -20 |
| 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 | A080663 | 1 -2 -11 -26 -47 -74 -107 -146 -191 -242 -299 -362 -431 -506 -587 -674 -767 -866 -971 -1082 -1199 |
| Inv:Rev | PolyCol2∑ k=0..n T(n, k) 2^k | A362176 | 1 1 -3 -11 25 201 -299 -5123 3249 167185 50221 -6637179 -8846903 309737689 769776645 -16575533939 |
| Inv:Rev | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 1 -8 -26 190 1126 -7424 -68228 399484 5311900 -27046304 -505117304 2172466792 56725135624 |
| Inv:Rev | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 1 -3 -26 673 9126 -642059 -12102068 1652365569 40012012828 -8980643704499 -265918023543864 |
| << | 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.