OEIS Similars: A359364
| ↕ Type | ↕ Trait | ↕ Anum | ↕ Sequence |
|---|---|---|---|
| Std | TriangleT(n, k), 0 ≤ k ≤ n | A359364 | 1 1 0 1 0 1 1 0 3 0 1 0 6 0 2 1 0 10 0 10 0 1 0 15 0 30 0 5 1 0 21 0 70 0 35 0 1 0 28 0 140 0 140 0 |
| Std | RevT(n, n - k), 0 ≤ k ≤ n | A097610 | 1 0 1 1 0 1 0 3 0 1 2 0 6 0 1 0 10 0 10 0 1 5 0 30 0 15 0 1 0 35 0 70 0 21 0 1 14 0 140 0 140 0 28 |
| Std | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | missing | 1 0 1 -1 0 1 0 -3 0 1 4 0 -6 0 1 0 20 0 -10 0 1 -35 0 60 0 -15 0 1 0 -245 0 140 0 -21 0 1 546 0 |
| Std | Accsee docs | missing | 1 1 1 1 1 2 1 1 4 4 1 1 7 7 9 1 1 11 11 21 21 1 1 16 16 46 46 51 1 1 22 22 92 92 127 127 1 1 29 29 |
| Std | AccRevsee docs | missing | 1 0 1 1 1 2 0 3 3 4 2 2 8 8 9 0 10 10 20 20 21 5 5 35 35 50 50 51 0 35 35 105 105 126 126 127 14 14 |
| Std | 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 2 1 0 21 0 10 1 0 28 0 30 0 1 0 36 0 70 0 1 0 45 |
| Std | Diffx1T(n, k) (k+1) | missing | 1 1 0 1 0 3 1 0 9 0 1 0 18 0 10 1 0 30 0 50 0 1 0 45 0 150 0 35 1 0 63 0 350 0 245 0 1 0 84 0 700 0 |
| Std | RowSum∑ k=0..n T(n, k) | A001006 | 1 1 2 4 9 21 51 127 323 835 2188 5798 15511 41835 113634 310572 853467 2356779 6536382 18199284 |
| Std | EvenSum∑ k=0..n T(n, k) even(k) | A001006 | 1 1 2 4 9 21 51 127 323 835 2188 5798 15511 41835 113634 310572 853467 2356779 6536382 18199284 |
| Std | AltSum∑ k=0..n T(n, k) (-1)^k | A001006 | 1 1 2 4 9 21 51 127 323 835 2188 5798 15511 41835 113634 310572 853467 2356779 6536382 18199284 |
| Std | AbsSum∑ k=0..n | T(n, k) | | A001006 | 1 1 2 4 9 21 51 127 323 835 2188 5798 15511 41835 113634 310572 853467 2356779 6536382 18199284 |
| Std | DiagSum∑ k=0..n // 2 T(n - k, k) | A023426 | 1 1 1 1 2 4 7 11 18 32 59 107 191 343 627 1159 2146 3972 7373 13757 25781 48437 91165 171945 325096 |
| Std | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A189912 | 1 2 4 10 25 66 177 484 1339 3742 10538 29866 85087 243478 699324 2015082 5822619 16865718 48958404 |
| Std | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A025179 | 1 1 4 10 29 81 231 659 1891 5443 15718 45508 132067 384047 1118820 3264642 9539787 27913083 |
| Std | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 1 3 6 10 30 210 140 1260 6300 4620 13860 180180 420420 6306300 5045040 4084080 36756720 |
| Std | RowGcdGcd k=0..n | T(n, k) | > 1 | missing | 1 1 1 3 2 10 5 7 14 6 3 11 66 26 13 1 2 34 17 19 38 2 1 23 46 10 5 3 6 58 435 155 62 2 1 1 6 222 37 |
| Std | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 1 3 6 10 30 70 140 420 1050 2310 6930 18018 42042 126126 336336 816816 2450448 6651216 16628040 |
| Std | ColMiddleT(n, n // 2) | missing | 1 1 0 0 6 10 0 0 140 252 0 0 4620 8580 0 0 180180 340340 0 0 7759752 14814072 0 0 356948592 |
| Std | CentralET(2 n, n) | A359647 | 1 0 6 0 140 0 4620 0 180180 0 7759752 0 356948592 0 17210021400 0 859544957700 0 44123307828600 0 |
| Std | CentralOT(2 n + 1, n) | missing | 1 0 10 0 252 0 8580 0 340340 0 14814072 0 686439600 0 33272708040 0 1668528447300 0 85924336297800 |
| 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) | 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 | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 1 2 10 39 151 681 3137 14519 69463 339118 1674278 8376721 42398721 216532018 1114896954 |
| Std | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -1 2 -10 39 -151 681 -3137 14519 -69463 339118 -1674278 8376721 -42398721 216532018 -1114896954 |
| Std | TransNat0∑ k=0..n T(n, k) k | missing | 0 0 2 6 20 60 180 532 1568 4608 13530 39710 116556 342212 1005186 2954070 8686320 25556304 75232854 |
| Std | TransNat1∑ k=0..n T(n, k) (k + 1) | A025179 | 1 1 4 10 29 81 231 659 1891 5443 15718 45508 132067 384047 1118820 3264642 9539787 27913083 |
| Std | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 0 4 12 56 200 720 2464 8288 27360 89220 287980 922152 2933528 9281636 29233260 91716000 286789728 |
| Std | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A000108 | 1 2 5 14 42 132 429 1430 4862 16796 58786 208012 742900 2674440 9694845 35357670 129644790 |
| Std | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A000108 | 1 -2 5 -14 42 -132 429 -1430 4862 -16796 58786 -208012 742900 -2674440 9694845 -35357670 129644790 |
| Std | DiagRow1T(n + 1, n) | A138364 | 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 0 |
| Std | DiagRow2T(n + 2, n) | A002457 | 1 0 6 0 30 0 140 0 630 0 2772 0 12012 0 51480 0 218790 0 923780 0 3879876 0 16224936 0 67603900 0 |
| Std | DiagRow3T(n + 3, n) | A002802 | 1 0 10 0 70 0 420 0 2310 0 12012 0 60060 0 291720 0 1385670 0 6466460 0 29745716 0 135207800 0 |
| 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 | Polysee docs | missing | 1 1 1 1 1 1 1 2 1 1 1 4 5 1 1 1 9 13 10 1 1 1 21 57 28 17 1 1 1 51 201 217 49 26 1 1 1 127 861 901 |
| Std | 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 |
| 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 | 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 |
| Std | PolyCol2∑ k=0..n T(n, k) 2^k | A091147 | 1 1 5 13 57 201 861 3445 14897 63313 278389 1223069 5465065 24513945 111037005 505298565 2314343265 |
| Std | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 1 10 28 217 901 6211 31375 205507 1153603 7413364 44174494 282750535 1745836795 11205047530 |
| Std | PolyDiag∑ k=0..n T(n, k) n^k | A359649 | 1 1 5 28 609 6501 272701 4286815 272156417 5648748355 484054204501 12482361156398 1351553781736225 |
| Alt | TriangleT(n, k), 0 ≤ k ≤ n | A359364 | 1 1 0 1 0 1 1 0 3 0 1 0 6 0 2 1 0 10 0 10 0 1 0 15 0 30 0 5 1 0 21 0 70 0 35 0 1 0 28 0 140 0 140 0 |
| Alt | RevT(n, n - k), 0 ≤ k ≤ n | A097610 | 1 0 1 1 0 1 0 3 0 1 2 0 6 0 1 0 10 0 10 0 1 5 0 30 0 15 0 1 0 35 0 70 0 21 0 1 14 0 140 0 140 0 28 |
| Alt | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | missing | 1 0 1 -1 0 1 0 -3 0 1 4 0 -6 0 1 0 20 0 -10 0 1 -35 0 60 0 -15 0 1 0 -245 0 140 0 -21 0 1 546 0 |
| Alt | Accsee docs | missing | 1 1 1 1 1 2 1 1 4 4 1 1 7 7 9 1 1 11 11 21 21 1 1 16 16 46 46 51 1 1 22 22 92 92 127 127 1 1 29 29 |
| Alt | AccRevsee docs | missing | 1 0 1 1 1 2 0 3 3 4 2 2 8 8 9 0 10 10 20 20 21 5 5 35 35 50 50 51 0 35 35 105 105 126 126 127 14 14 |
| Alt | 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 2 1 0 21 0 10 1 0 28 0 30 0 1 0 36 0 70 0 1 0 45 |
| Alt | Diffx1T(n, k) (k+1) | missing | 1 1 0 1 0 3 1 0 9 0 1 0 18 0 10 1 0 30 0 50 0 1 0 45 0 150 0 35 1 0 63 0 350 0 245 0 1 0 84 0 700 0 |
| Alt | RowSum∑ k=0..n T(n, k) | A001006 | 1 1 2 4 9 21 51 127 323 835 2188 5798 15511 41835 113634 310572 853467 2356779 6536382 18199284 |
| Alt | EvenSum∑ k=0..n T(n, k) even(k) | A001006 | 1 1 2 4 9 21 51 127 323 835 2188 5798 15511 41835 113634 310572 853467 2356779 6536382 18199284 |
| Alt | AltSum∑ k=0..n T(n, k) (-1)^k | A001006 | 1 1 2 4 9 21 51 127 323 835 2188 5798 15511 41835 113634 310572 853467 2356779 6536382 18199284 |
| Alt | AbsSum∑ k=0..n | T(n, k) | | A001006 | 1 1 2 4 9 21 51 127 323 835 2188 5798 15511 41835 113634 310572 853467 2356779 6536382 18199284 |
| Alt | DiagSum∑ k=0..n // 2 T(n - k, k) | A023426 | 1 1 1 1 2 4 7 11 18 32 59 107 191 343 627 1159 2146 3972 7373 13757 25781 48437 91165 171945 325096 |
| Alt | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A189912 | 1 2 4 10 25 66 177 484 1339 3742 10538 29866 85087 243478 699324 2015082 5822619 16865718 48958404 |
| Alt | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A025179 | 1 1 4 10 29 81 231 659 1891 5443 15718 45508 132067 384047 1118820 3264642 9539787 27913083 |
| Alt | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 1 3 6 10 30 210 140 1260 6300 4620 13860 180180 420420 6306300 5045040 4084080 36756720 |
| Alt | RowGcdGcd k=0..n | T(n, k) | > 1 | missing | 1 1 1 3 2 10 5 7 14 6 3 11 66 26 13 1 2 34 17 19 38 2 1 23 46 10 5 3 6 58 435 155 62 2 1 1 6 222 37 |
| Alt | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 1 3 6 10 30 70 140 420 1050 2310 6930 18018 42042 126126 336336 816816 2450448 6651216 16628040 |
| Alt | ColMiddleT(n, n // 2) | missing | 1 1 0 0 6 10 0 0 140 252 0 0 4620 8580 0 0 180180 340340 0 0 7759752 14814072 0 0 356948592 |
| Alt | CentralET(2 n, n) | A359647 | 1 0 6 0 140 0 4620 0 180180 0 7759752 0 356948592 0 17210021400 0 859544957700 0 44123307828600 0 |
| Alt | CentralOT(2 n + 1, n) | missing | 1 0 10 0 252 0 8580 0 340340 0 14814072 0 686439600 0 33272708040 0 1668528447300 0 85924336297800 |
| Alt | ColLeftT(n, 0) | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Alt | ColRightT(n, n) | 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) | missing | 1 1 2 10 39 151 681 3137 14519 69463 339118 1674278 8376721 42398721 216532018 1114896954 |
| Alt | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -1 2 -10 39 -151 681 -3137 14519 -69463 339118 -1674278 8376721 -42398721 216532018 -1114896954 |
| Alt | TransNat0∑ k=0..n T(n, k) k | missing | 0 0 2 6 20 60 180 532 1568 4608 13530 39710 116556 342212 1005186 2954070 8686320 25556304 75232854 |
| Alt | TransNat1∑ k=0..n T(n, k) (k + 1) | A025179 | 1 1 4 10 29 81 231 659 1891 5443 15718 45508 132067 384047 1118820 3264642 9539787 27913083 |
| Alt | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 0 4 12 56 200 720 2464 8288 27360 89220 287980 922152 2933528 9281636 29233260 91716000 286789728 |
| Alt | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A000108 | 1 2 5 14 42 132 429 1430 4862 16796 58786 208012 742900 2674440 9694845 35357670 129644790 |
| Alt | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A000108 | 1 -2 5 -14 42 -132 429 -1430 4862 -16796 58786 -208012 742900 -2674440 9694845 -35357670 129644790 |
| Alt | DiagRow1T(n + 1, n) | A138364 | 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 0 |
| Alt | DiagRow2T(n + 2, n) | A002457 | 1 0 6 0 30 0 140 0 630 0 2772 0 12012 0 51480 0 218790 0 923780 0 3879876 0 16224936 0 67603900 0 |
| Alt | DiagRow3T(n + 3, n) | A002802 | 1 0 10 0 70 0 420 0 2310 0 12012 0 60060 0 291720 0 1385670 0 6466460 0 29745716 0 135207800 0 |
| 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 | Polysee docs | missing | 1 1 1 1 1 1 1 2 1 1 1 4 5 1 1 1 9 13 10 1 1 1 21 57 28 17 1 1 1 51 201 217 49 26 1 1 1 127 861 901 |
| Alt | 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 |
| 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 | 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 |
| Alt | PolyCol2∑ k=0..n T(n, k) 2^k | A091147 | 1 1 5 13 57 201 861 3445 14897 63313 278389 1223069 5465065 24513945 111037005 505298565 2314343265 |
| Alt | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 1 10 28 217 901 6211 31375 205507 1153603 7413364 44174494 282750535 1745836795 11205047530 |
| Alt | PolyDiag∑ k=0..n T(n, k) n^k | A359649 | 1 1 5 28 609 6501 272701 4286815 272156417 5648748355 484054204501 12482361156398 1351553781736225 |
| Rev | TriangleT(n, k), 0 ≤ k ≤ n | A097610 | 1 0 1 1 0 1 0 3 0 1 2 0 6 0 1 0 10 0 10 0 1 5 0 30 0 15 0 1 0 35 0 70 0 21 0 1 14 0 140 0 140 0 28 |
| Rev | InvT-1(n, k), 0 ≤ k ≤ n | missing | 1 0 1 -1 0 1 0 -3 0 1 4 0 -6 0 1 0 20 0 -10 0 1 -35 0 60 0 -15 0 1 0 -245 0 140 0 -21 0 1 546 0 |
| Rev | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 0 1 0 -1 1 0 -3 0 1 0 -6 0 4 1 0 -10 0 20 0 1 0 -15 0 60 0 -35 1 0 -21 0 140 0 -245 0 1 0 -28 0 |
| Rev | Accsee docs | missing | 1 0 1 1 1 2 0 3 3 4 2 2 8 8 9 0 10 10 20 20 21 5 5 35 35 50 50 51 0 35 35 105 105 126 126 127 14 14 |
| Rev | AccRevsee docs | missing | 1 1 1 1 1 2 1 1 4 4 1 1 7 7 9 1 1 11 11 21 21 1 1 16 16 46 46 51 1 1 22 22 92 92 127 127 1 1 29 29 |
| Rev | AntiDiagsee docs | missing | 1 0 1 1 0 0 2 3 1 0 0 0 5 10 6 1 0 0 0 0 14 35 30 10 1 0 0 0 0 0 42 126 140 70 15 1 0 0 0 0 0 0 132 |
| Rev | Diffx1T(n, k) (k+1) | missing | 1 0 2 1 0 3 0 6 0 4 2 0 18 0 5 0 20 0 40 0 6 5 0 90 0 75 0 7 0 70 0 280 0 126 0 8 14 0 420 0 700 0 |
| Rev | RowSum∑ k=0..n T(n, k) | A001006 | 1 1 2 4 9 21 51 127 323 835 2188 5798 15511 41835 113634 310572 853467 2356779 6536382 18199284 |
| Rev | EvenSum∑ k=0..n T(n, k) even(k) | A026945 | 1 0 2 0 9 0 51 0 323 0 2188 0 15511 0 113634 0 853467 0 6536382 0 50852019 0 400763223 0 3192727797 |
| Rev | OddSum∑ k=0..n T(n, k) odd(k) | A099250 | 0 1 0 4 0 21 0 127 0 835 0 5798 0 41835 0 310572 0 2356779 0 18199284 0 142547559 0 1129760415 0 |
| Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A001006 | 1 -1 2 -4 9 -21 51 -127 323 -835 2188 -5798 15511 -41835 113634 -310572 853467 -2356779 6536382 |
| Rev | AbsSum∑ k=0..n | T(n, k) | | A001006 | 1 1 2 4 9 21 51 127 323 835 2188 5798 15511 41835 113634 310572 853467 2356779 6536382 18199284 |
| Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | A006318 | 1 0 2 0 6 0 22 0 90 0 394 0 1806 0 8558 0 41586 0 206098 0 1037718 0 5293446 0 27297738 0 142078746 |
| Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A025179 | 1 1 4 10 29 81 231 659 1891 5443 15718 45508 132067 384047 1118820 3264642 9539787 27913083 |
| Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A189912 | 1 2 4 10 25 66 177 484 1339 3742 10538 29866 85087 243478 699324 2015082 5822619 16865718 48958404 |
| Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 1 3 6 10 30 210 140 1260 6300 4620 13860 180180 420420 6306300 5045040 4084080 36756720 |
| Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | missing | 1 1 1 3 2 10 5 7 14 6 3 11 66 26 13 1 2 34 17 19 38 2 1 23 46 10 5 3 6 58 435 155 62 2 1 1 6 222 37 |
| Rev | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 1 3 6 10 30 70 140 420 1050 2310 6930 18018 42042 126126 336336 816816 2450448 6651216 16628040 |
| Rev | ColMiddleT(n, n // 2) | missing | 1 0 0 3 6 0 0 70 140 0 0 2310 4620 0 0 90090 180180 0 0 3879876 7759752 0 0 178474296 356948592 0 0 |
| Rev | CentralET(2 n, n) | A359647 | 1 0 6 0 140 0 4620 0 180180 0 7759752 0 356948592 0 17210021400 0 859544957700 0 44123307828600 0 |
| Rev | CentralOT(2 n + 1, n) | missing | 0 3 0 70 0 2310 0 90090 0 3879876 0 178474296 0 8605010700 0 429772478850 0 22061653914300 0 |
| Rev | 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 |
| Rev | ColRightT(n, n) | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Rev | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 1 2 10 39 151 681 3137 14519 69463 339118 1674278 8376721 42398721 216532018 1114896954 |
| Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 1 2 10 39 151 681 3137 14519 69463 339118 1674278 8376721 42398721 216532018 1114896954 |
| Rev | TransNat0∑ k=0..n T(n, k) k | A005717 | 0 1 2 6 16 45 126 357 1016 2907 8350 24068 69576 201643 585690 1704510 4969152 14508939 42422022 |
| Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | A189912 | 1 2 4 10 25 66 177 484 1339 3742 10538 29866 85087 243478 699324 2015082 5822619 16865718 48958404 |
| Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 4 12 40 125 396 1239 3872 12051 37420 115918 358392 1106131 3408692 10489860 32241312 98984523 |
| Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A091147 | 1 1 5 13 57 201 861 3445 14897 63313 278389 1223069 5465065 24513945 111037005 505298565 2314343265 |
| Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A091147 | 1 1 5 13 57 201 861 3445 14897 63313 278389 1223069 5465065 24513945 111037005 505298565 2314343265 |
| Rev | DiagRow2T(n + 2, n) | A000217 | 1 3 6 10 15 21 28 36 45 55 66 78 91 105 120 136 153 171 190 210 231 253 276 300 325 351 378 406 435 |
| Rev | DiagCol1T(n + 1, 1) | A138364 | 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 0 |
| Rev | DiagCol2T(n + 2, 2) | A002457 | 1 0 6 0 30 0 140 0 630 0 2772 0 12012 0 51480 0 218790 0 923780 0 3879876 0 16224936 0 67603900 0 |
| Rev | DiagCol3T(n + 3, 3) | A002802 | 1 0 10 0 70 0 420 0 2310 0 12012 0 60060 0 291720 0 1385670 0 6466460 0 29745716 0 135207800 0 |
| Rev | Polysee docs | A247495 | 1 0 1 1 1 1 0 2 2 1 2 4 5 3 1 0 9 14 10 4 1 5 21 42 36 17 5 1 0 51 132 137 76 26 6 1 14 127 429 543 |
| Rev | 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 |
| 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 | A079908 | 0 4 14 36 76 140 234 364 536 756 1030 1364 1764 2236 2786 3420 4144 4964 5886 6916 8060 9324 10714 |
| Rev | PolyCol2∑ k=0..n T(n, k) 2^k | A000108 | 1 2 5 14 42 132 429 1430 4862 16796 58786 208012 742900 2674440 9694845 35357670 129644790 |
| Rev | PolyCol3∑ k=0..n T(n, k) 3^k | A002212 | 1 3 10 36 137 543 2219 9285 39587 171369 751236 3328218 14878455 67030785 304036170 1387247580 |
| Rev | PolyDiag∑ k=0..n T(n, k) n^k | A247496 | 1 1 5 36 354 4425 67181 1200745 24699662 574795035 14930563042 428235433978 13442267711940 |
| Rev:Inv | TriangleT(n, k), 0 ≤ k ≤ n | missing | 1 0 1 -1 0 1 0 -3 0 1 4 0 -6 0 1 0 20 0 -10 0 1 -35 0 60 0 -15 0 1 0 -245 0 140 0 -21 0 1 546 0 |
| Rev:Inv | RevT(n, n - k), 0 ≤ k ≤ n | missing | 1 1 0 1 0 -1 1 0 -3 0 1 0 -6 0 4 1 0 -10 0 20 0 1 0 -15 0 60 0 -35 1 0 -21 0 140 0 -245 0 1 0 -28 0 |
| Rev:Inv | InvT-1(n, k), 0 ≤ k ≤ n | A097610 | 1 0 1 1 0 1 0 3 0 1 2 0 6 0 1 0 10 0 10 0 1 5 0 30 0 15 0 1 0 35 0 70 0 21 0 1 14 0 140 0 140 0 28 |
| Rev:Inv | RevInvT-1(n, n - k), 0 ≤ k ≤ n | A359364 | 1 1 0 1 0 1 1 0 3 0 1 0 6 0 2 1 0 10 0 10 0 1 0 15 0 30 0 5 1 0 21 0 70 0 35 0 1 0 28 0 140 0 140 0 |
| Rev:Inv | Accsee docs | missing | 1 0 1 -1 -1 0 0 -3 -3 -2 4 4 -2 -2 -1 0 20 20 10 10 11 -35 -35 25 25 10 10 11 0 -245 -245 -105 -105 |
| Rev:Inv | AccRevsee docs | missing | 1 1 1 1 1 0 1 1 -2 -2 1 1 -5 -5 -1 1 1 -9 -9 11 11 1 1 -14 -14 46 46 11 1 1 -20 -20 120 120 -125 |
| Rev:Inv | AntiDiagsee docs | missing | 1 0 -1 1 0 0 4 -3 1 0 0 0 -35 20 -6 1 0 0 0 0 546 -245 60 -10 1 0 0 0 0 0 -13482 4914 -980 140 -15 |
| Rev:Inv | Diffx1T(n, k) (k+1) | missing | 1 0 2 -1 0 3 0 -6 0 4 4 0 -18 0 5 0 40 0 -40 0 6 -35 0 180 0 -75 0 7 0 -490 0 560 0 -126 0 8 546 0 |
| Rev:Inv | RowSum∑ k=0..n T(n, k) | A308846 | 1 1 0 -2 -1 11 11 -125 -181 2443 4534 -73116 -164075 3106169 8150624 -177689590 -533231545 |
| Rev:Inv | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 0 0 0 -1 0 11 0 -181 0 4534 0 -164075 0 8150624 0 -533231545 0 44461467464 0 -4603245727023 0 |
| Rev:Inv | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 1 0 -2 0 11 0 -125 0 2443 0 -73116 0 3106169 0 -177689590 0 13167063415 0 -1226832808294 0 |
| Rev:Inv | AltSum∑ k=0..n T(n, k) (-1)^k | A308846 | 1 -1 0 2 -1 -11 11 125 -181 -2443 4534 73116 -164075 -3106169 8150624 177689590 -533231545 |
| Rev:Inv | AbsSum∑ k=0..n | T(n, k) | | missing | 1 1 2 4 11 31 111 407 1835 8395 46288 255938 1680361 10938149 83569006 626889252 5469300087 |
| Rev:Inv | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 0 0 0 2 0 -20 0 352 0 -9422 0 359480 0 -18598512 0 1255664060 0 -107332663328 0 11337290575470 0 |
| Rev:Inv | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 1 -2 -8 3 71 11 -1077 -629 26059 25444 -927266 -1255583 45619341 78772994 -2965292800 -6221902825 |
| Rev:Inv | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 2 2 -2 -9 6 77 -48 -1181 814 28964 -23242 -1041467 973194 51636990 -55430230 -3376264985 |
| Rev:Inv | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 1 3 12 20 420 2940 76440 687960 368058600 269909640 165589564140 307523476260 |
| Rev:Inv | RowGcdGcd k=0..n | T(n, k) | > 1 | missing | 1 1 1 3 2 10 5 7 14 6 3 11 66 26 13 1 2 34 17 19 38 2 1 23 46 10 5 3 6 58 435 155 62 2 1 1 6 222 37 |
| Rev:Inv | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 1 3 6 20 60 245 980 4914 24570 148302 889812 6316596 44216172 361627695 2893021560 26803501010 |
| Rev:Inv | ColMiddleT(n, n // 2) | missing | 1 0 0 -3 -6 0 0 140 280 0 0 -16170 -32340 0 0 3513510 7027020 0 0 -1245440196 -2490880392 0 0 |
| Rev:Inv | CentralET(2 n, n) | missing | 1 0 -6 0 280 0 -32340 0 7027020 0 -2490880392 0 1313927767152 0 -967151572615800 0 |
| Rev:Inv | CentralOT(2 n + 1, n) | missing | 0 -3 0 140 0 -16170 0 3513510 0 -1245440196 0 656963883576 0 -483575786307900 0 473854671778123350 |
| Rev:Inv | ColLeftT(n, 0) | A238390 | 1 0 -1 0 4 0 -35 0 546 0 -13482 0 485892 0 -24108513 0 1576676530 0 -131451399794 0 13609184032808 |
| Rev:Inv | ColRightT(n, n) | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Rev:Inv | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 1 0 -8 -31 1 641 2745 -8077 -140525 -276956 6195564 46635535 -217304593 -4897212020 -4673293612 |
| Rev:Inv | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 1 0 -8 -31 1 641 2745 -8077 -140525 -276956 6195564 46635535 -217304593 -4897212020 -4673293612 |
| Rev:Inv | TransNat0∑ k=0..n T(n, k) k | missing | 0 1 2 0 -8 -5 66 77 -1000 -1629 24430 49874 -877392 -2132975 43486366 122259360 -2843033440 |
| Rev:Inv | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 2 2 -2 -9 6 77 -48 -1181 814 28964 -23242 -1041467 973194 51636990 -55430230 -3376264985 |
| Rev:Inv | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 4 6 -8 -45 36 539 -384 -10629 8140 318604 -278904 -13539071 13624716 774554850 -886883680 |
| Rev:Inv | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 1 -3 -11 41 281 -1339 -13523 81425 1077745 -7972787 -129812187 1146196921 22100478089 |
| Rev:Inv | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 1 -3 -11 41 281 -1339 -13523 81425 1077745 -7972787 -129812187 1146196921 22100478089 |
| Rev: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 |
| Rev:Inv | DiagCol1T(n + 1, 1) | missing | 1 0 -3 0 20 0 -245 0 4914 0 -148302 0 6316596 0 -361627695 0 26803501010 0 -2497576596086 0 |
| Rev:Inv | DiagCol2T(n + 2, 2) | missing | 1 0 -6 0 60 0 -980 0 24570 0 -889812 0 44216172 0 -2893021560 0 241231509090 0 -24975765960860 0 |
| Rev:Inv | DiagCol3T(n + 3, 3) | missing | 1 0 -10 0 140 0 -2940 0 90090 0 -3855852 0 221080860 0 -16393788840 0 1527799557570 0 |
| Rev:Inv | Polysee docs | missing | 1 0 1 -1 1 1 0 0 2 1 4 -2 3 3 1 0 -1 2 8 4 1 -35 11 -4 18 15 5 1 0 11 -8 31 52 24 6 1 546 -125 29 |
| Rev: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 |
| Rev: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 |
| Rev: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 |
| Rev:Inv | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 2 3 2 -4 -8 29 86 -430 -1660 10462 49524 -375404 -2102072 18602159 120219586 -1216092718 |
| Rev:Inv | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 3 8 18 31 33 19 129 555 -1215 -11538 39636 418581 -1682613 -20740776 96338214 1356035527 |
| Rev:Inv | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 1 3 18 164 1975 29341 516901 10521890 242895267 6268943518 178861697124 5589828116676 |
| << | 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.