OEIS Similars: A122538, A033877, A080245, A080247, A106579
| ↕ Type | ↕ Trait | ↕ Anum | ↕ Sequence |
|---|---|---|---|
| Std | TriangleT(n, k), 0 ≤ k ≤ n | A122538 | 1 0 1 0 2 1 0 6 4 1 0 22 16 6 1 0 90 68 30 8 1 0 394 304 146 48 10 1 0 1806 1412 714 264 70 12 1 0 |
| Std | RevT(n, n - k), 0 ≤ k ≤ n | A106579 | 1 1 0 1 2 0 1 4 6 0 1 6 16 22 0 1 8 30 68 90 0 1 10 48 146 304 394 0 1 12 70 264 714 1412 1806 0 1 |
| Std | Accsee docs | missing | 1 0 1 0 2 3 0 6 10 11 0 22 38 44 45 0 90 158 188 196 197 0 394 698 844 892 902 903 0 1806 3218 3932 |
| Std | AccRevsee docs | A144944 | 1 1 1 1 3 3 1 5 11 11 1 7 23 45 45 1 9 39 107 197 197 1 11 59 205 509 903 903 1 13 83 347 1061 2473 |
| Std | AntiDiagsee docs | missing | 1 0 0 1 0 2 0 6 1 0 22 4 0 90 16 1 0 394 68 6 0 1806 304 30 1 0 8558 1412 146 8 0 41586 6752 714 48 |
| Std | Diffx1T(n, k) (k+1) | missing | 1 0 2 0 4 3 0 12 12 4 0 44 48 24 5 0 180 204 120 40 6 0 788 912 584 240 60 7 0 3612 4236 2856 1320 |
| Std | RowSum∑ k=0..n T(n, k) | A001003 | 1 1 3 11 45 197 903 4279 20793 103049 518859 2646723 13648869 71039373 372693519 1968801519 |
| Std | EvenSum∑ k=0..n T(n, k) even(k) | A239204 | 1 0 1 4 17 76 353 1688 8257 41128 207905 1063932 5501073 28695252 150827073 798054000 4247388417 |
| Std | OddSum∑ k=0..n T(n, k) odd(k) | A010683 | 0 1 2 7 28 121 550 2591 12536 61921 310954 1582791 8147796 42344121 221866446 1170747519 6216189936 |
| Std | AltSum∑ k=0..n T(n, k) (-1)^k | A001003 | 1 -1 -1 -3 -11 -45 -197 -903 -4279 -20793 -103049 -518859 -2646723 -13648869 -71039373 -372693519 |
| Std | AbsSum∑ k=0..n | T(n, k) | | A001003 | 1 1 3 11 45 197 903 4279 20793 103049 518859 2646723 13648869 71039373 372693519 1968801519 |
| Std | DiagSum∑ k=0..n // 2 T(n - k, k) | A006603 | 1 0 1 2 7 26 107 468 2141 10124 49101 242934 1221427 6222838 32056215 166690696 873798681 |
| Std | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 1 5 27 149 829 4633 25975 146009 822585 4643517 26259603 148740045 843724149 4792348785 |
| Std | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A010683 | 1 2 7 28 121 550 2591 12536 61921 310954 1582791 8147796 42344121 221866446 1170747519 6216189936 |
| Std | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 2 12 528 6120 65577360 2384317320 307331984910720 10705170228466855130640 |
| Std | RowGcdGcd k=0..n | T(n, k) | > 1 | A055642 | 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 |
| Std | RowMaxMax k=0..n | T(n, k) | | A006318 | 1 1 2 6 22 90 394 1806 8558 41586 206098 1037718 5293446 27297738 142078746 745387038 3937603038 |
| Std | ColMiddleT(n, n // 2) | missing | 1 0 2 6 16 68 146 714 1408 7432 14002 77550 142000 812940 1459810 8561938 15158272 90560528 |
| Std | CentralET(2 n, n) | A103885 | 1 2 16 146 1408 14002 142000 1459810 15158272 158611106 1669752016 17664712562 187641279616 |
| Std | CentralOT(2 n + 1, n) | missing | 0 6 68 714 7432 77550 812940 8561938 90560528 961474518 10241444820 109402827226 1171617940248 |
| Std | ColLeftT(n, 0) | 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 | 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) | A178792 | 1 1 5 31 209 1471 10625 78079 580865 4361215 32978945 250806271 1916280833 14698053631 113104519169 |
| Std | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A000225 | 1 1 -3 7 -15 31 -63 127 -255 511 -1023 2047 -4095 8191 -16383 32767 -65535 131071 -262143 524287 |
| Std | TransNat0∑ k=0..n T(n, k) k | A239204 | 0 1 4 17 76 353 1688 8257 41128 207905 1063932 5501073 28695252 150827073 798054000 4247388417 |
| Std | TransNat1∑ k=0..n T(n, k) (k + 1) | A010683 | 1 2 7 28 121 550 2591 12536 61921 310954 1582791 8147796 42344121 221866446 1170747519 6216189936 |
| Std | TransSqrs∑ k=0..n T(n, k) k^2 | A065096 | 0 1 6 31 156 785 3978 20335 104856 545073 2854350 15046383 79787700 425360481 2278586898 |
| Std | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A330802 | 1 1 5 33 253 2121 18853 174609 1667021 16290969 162171445 1638732129 16765758429 173325794409 |
| Std | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A330803 | 1 1 -3 17 -123 1001 -8739 79969 -756939 7349657 -72798003 732681489 -7471545435 77031538377 |
| Std | DiagRow1T(n + 1, n) | A005843 | 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 |
| Std | DiagRow2T(n + 2, n) | A054000 | 0 6 16 30 48 70 96 126 160 198 240 286 336 390 448 510 576 646 720 798 880 966 1056 1150 1248 1350 |
| Std | DiagRow3T(n + 3, n) | missing | 0 22 68 146 264 430 652 938 1296 1734 2260 2882 3608 4446 5404 6490 7712 9078 10596 12274 14120 |
| Std | DiagCol1T(n + 1, 1) | A006318 | 1 2 6 22 90 394 1806 8558 41586 206098 1037718 5293446 27297738 142078746 745387038 3937603038 |
| Std | DiagCol2T(n + 2, 2) | A006319 | 1 4 16 68 304 1412 6752 33028 164512 831620 4255728 22004292 114781008 603308292 3192216000 |
| Std | DiagCol3T(n + 3, 3) | A006320 | 1 6 30 146 714 3534 17718 89898 461010 2386390 12455118 65478978 346448538 1843520670 9859734630 |
| Std | Polysee docs | missing | 1 0 1 0 1 1 0 3 2 1 0 11 8 3 1 0 45 36 15 4 1 0 197 172 81 24 5 1 0 903 852 453 152 35 6 1 0 4279 |
| 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 | A005563 | 0 3 8 15 24 35 48 63 80 99 120 143 168 195 224 255 288 323 360 399 440 483 528 575 624 675 728 783 |
| Std | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 0 11 36 81 152 255 396 581 816 1107 1460 1881 2376 2951 3612 4365 5216 6171 7236 8417 9720 11151 |
| Std | PolyCol2∑ k=0..n T(n, k) 2^k | A109980 | 1 2 8 36 172 852 4324 22332 116876 618084 3296308 17702412 95627580 519170004 2830862532 |
| Std | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 3 15 81 453 2583 14907 86733 507561 2982987 17588775 103976073 615916269 3654551007 21714187923 |
| Std | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 1 8 81 984 14025 231468 4372417 93470576 2237080977 59360130180 1731243895953 55079997072840 |
| Alt | TriangleT(n, k), 0 ≤ k ≤ n | A122538 | 1 0 -1 0 -2 1 0 -6 4 -1 0 -22 16 -6 1 0 -90 68 -30 8 -1 0 -394 304 -146 48 -10 1 0 -1806 1412 -714 |
| Alt | RevT(n, n - k), 0 ≤ k ≤ n | A106579 | 1 -1 0 1 -2 0 -1 4 -6 0 1 -6 16 -22 0 -1 8 -30 68 -90 0 1 -10 48 -146 304 -394 0 -1 12 -70 264 -714 |
| Alt | InvT-1(n, k), 0 ≤ k ≤ n | missing | 1 0 1 0 2 1 0 -2 -4 1 0 -22 -40 6 1 0 70 132 -18 -8 1 0 1250 2352 -322 -128 10 1 0 -6738 -12692 |
| Alt | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 0 1 2 0 1 -4 -2 0 1 6 -40 -22 0 1 -8 -18 132 70 0 1 10 -128 -322 2352 1250 0 1 -12 -50 712 1734 |
| Alt | Accsee docs | missing | 1 0 -1 0 -2 -1 0 -6 -2 -3 0 -22 -6 -12 -11 0 -90 -22 -52 -44 -45 0 -394 -90 -236 -188 -198 -197 0 |
| Alt | AccRevsee docs | missing | 1 -1 -1 1 -1 -1 -1 3 -3 -3 1 -5 11 -11 -11 -1 7 -23 45 -45 -45 1 -9 39 -107 197 -197 -197 -1 11 -59 |
| Alt | AntiDiagsee docs | missing | 1 0 0 -1 0 -2 0 -6 1 0 -22 4 0 -90 16 -1 0 -394 68 -6 0 -1806 304 -30 1 0 -8558 1412 -146 8 0 |
| Alt | Diffx1T(n, k) (k+1) | missing | 1 0 -2 0 -4 3 0 -12 12 -4 0 -44 48 -24 5 0 -180 204 -120 40 -6 0 -788 912 -584 240 -60 7 0 -3612 |
| Alt | RowSum∑ k=0..n T(n, k) | A001003 | 1 -1 -1 -3 -11 -45 -197 -903 -4279 -20793 -103049 -518859 -2646723 -13648869 -71039373 -372693519 |
| Alt | EvenSum∑ k=0..n T(n, k) even(k) | A239204 | 1 0 1 4 17 76 353 1688 8257 41128 207905 1063932 5501073 28695252 150827073 798054000 4247388417 |
| Alt | OddSum∑ k=0..n T(n, k) odd(k) | A010683 | 0 -1 -2 -7 -28 -121 -550 -2591 -12536 -61921 -310954 -1582791 -8147796 -42344121 -221866446 |
| Alt | AltSum∑ k=0..n T(n, k) (-1)^k | A001003 | 1 1 3 11 45 197 903 4279 20793 103049 518859 2646723 13648869 71039373 372693519 1968801519 |
| Alt | AbsSum∑ k=0..n | T(n, k) | | A001003 | 1 1 3 11 45 197 903 4279 20793 103049 518859 2646723 13648869 71039373 372693519 1968801519 |
| Alt | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 0 -1 -2 -5 -18 -75 -332 -1531 -7284 -35501 -176350 -889585 -4544710 -23466263 -122267608 |
| Alt | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 -1 -3 -11 -51 -253 -1303 -6871 -36823 -199673 -1092411 -6018403 -33343467 -185583093 -1036895343 |
| Alt | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 -2 -1 -4 -15 -62 -273 -1256 -5967 -29050 -144177 -726764 -3710655 -19149942 -99734625 -523520592 |
| Alt | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 2 12 528 6120 65577360 2384317320 307331984910720 10705170228466855130640 |
| Alt | RowGcdGcd k=0..n | T(n, k) | > 1 | A055642 | 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 |
| Alt | RowMaxMax k=0..n | T(n, k) | | A006318 | 1 1 2 6 22 90 394 1806 8558 41586 206098 1037718 5293446 27297738 142078746 745387038 3937603038 |
| Alt | ColMiddleT(n, n // 2) | missing | 1 0 -2 -6 16 68 -146 -714 1408 7432 -14002 -77550 142000 812940 -1459810 -8561938 15158272 90560528 |
| Alt | CentralET(2 n, n) | A103885 | 1 -2 16 -146 1408 -14002 142000 -1459810 15158272 -158611106 1669752016 -17664712562 187641279616 |
| Alt | CentralOT(2 n + 1, n) | missing | 0 -6 68 -714 7432 -77550 812940 -8561938 90560528 -961474518 10241444820 -109402827226 |
| Alt | ColLeftT(n, 0) | 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 | BinConv∑ k=0..n C(n, k) T(n, k) | A000225 | 1 -1 -3 -7 -15 -31 -63 -127 -255 -511 -1023 -2047 -4095 -8191 -16383 -32767 -65535 -131071 -262143 |
| Alt | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A178792 | 1 -1 5 -31 209 -1471 10625 -78079 580865 -4361215 32978945 -250806271 1916280833 -14698053631 |
| Alt | TransNat0∑ k=0..n T(n, k) k | A239204 | 0 -1 0 -1 -4 -17 -76 -353 -1688 -8257 -41128 -207905 -1063932 -5501073 -28695252 -150827073 |
| Alt | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 -2 -1 -4 -15 -62 -273 -1256 -5967 -29050 -144177 -726764 -3710655 -19149942 -99734625 -523520592 |
| Alt | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 -1 2 1 4 15 62 273 1256 5967 29050 144177 726764 3710655 19149942 99734625 523520592 2766855519 |
| Alt | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A330803 | 1 -1 -3 -17 -123 -1001 -8739 -79969 -756939 -7349657 -72798003 -732681489 -7471545435 -77031538377 |
| Alt | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A330802 | 1 -1 5 -33 253 -2121 18853 -174609 1667021 -16290969 162171445 -1638732129 16765758429 |
| Alt | DiagRow1T(n + 1, n) | A005843 | 0 -2 4 -6 8 -10 12 -14 16 -18 20 -22 24 -26 28 -30 32 -34 36 -38 40 -42 44 -46 48 -50 52 -54 56 -58 |
| Alt | DiagRow2T(n + 2, n) | A054000 | 0 -6 16 -30 48 -70 96 -126 160 -198 240 -286 336 -390 448 -510 576 -646 720 -798 880 -966 1056 |
| Alt | DiagRow3T(n + 3, n) | missing | 0 -22 68 -146 264 -430 652 -938 1296 -1734 2260 -2882 3608 -4446 5404 -6490 7712 -9078 10596 -12274 |
| Alt | DiagCol1T(n + 1, 1) | A006318 | -1 -2 -6 -22 -90 -394 -1806 -8558 -41586 -206098 -1037718 -5293446 -27297738 -142078746 -745387038 |
| Alt | DiagCol2T(n + 2, 2) | A006319 | 1 4 16 68 304 1412 6752 33028 164512 831620 4255728 22004292 114781008 603308292 3192216000 |
| Alt | DiagCol3T(n + 3, 3) | A006320 | -1 -6 -30 -146 -714 -3534 -17718 -89898 -461010 -2386390 -12455118 -65478978 -346448538 -1843520670 |
| Alt | Polysee docs | missing | 1 0 1 0 -1 1 0 -1 -2 1 0 -3 0 -3 1 0 -11 -4 3 -4 1 0 -45 -12 -9 8 -5 1 0 -197 -52 -3 -24 15 -6 1 0 |
| 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 | A005563 | 0 -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 |
| Alt | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 0 -3 -4 -9 -24 -55 -108 -189 -304 -459 -660 -913 -1224 -1599 -2044 -2565 -3168 -3859 -4644 -5529 |
| Alt | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 -2 0 -4 -12 -52 -228 -1052 -5004 -24388 -121140 -611052 -3121596 -16117428 -83974212 -440941884 |
| Alt | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 -3 3 -9 -3 -63 -201 -1053 -4839 -23931 -118677 -600273 -3069675 -15868791 -82755873 -434906469 |
| Alt | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 -1 0 -9 40 -625 8148 -142737 2814096 -63713601 1615812220 -45439774809 1402642106424 |
| Rev | TriangleT(n, k), 0 ≤ k ≤ n | A106579 | 1 1 0 1 2 0 1 4 6 0 1 6 16 22 0 1 8 30 68 90 0 1 10 48 146 304 394 0 1 12 70 264 714 1412 1806 0 1 |
| Rev | Accsee docs | A144944 | 1 1 1 1 3 3 1 5 11 11 1 7 23 45 45 1 9 39 107 197 197 1 11 59 205 509 903 903 1 13 83 347 1061 2473 |
| Rev | AccRevsee docs | missing | 1 0 1 0 2 3 0 6 10 11 0 22 38 44 45 0 90 158 188 196 197 0 394 698 844 892 902 903 0 1806 3218 3932 |
| Rev | AntiDiagsee docs | missing | 1 1 1 0 1 2 1 4 0 1 6 6 1 8 16 0 1 10 30 22 1 12 48 68 0 1 14 70 146 90 1 16 96 264 304 0 1 18 126 |
| Rev | Diffx1T(n, k) (k+1) | missing | 1 1 0 1 4 0 1 8 18 0 1 12 48 88 0 1 16 90 272 450 0 1 20 144 584 1520 2364 0 1 24 210 1056 3570 |
| Rev | RowSum∑ k=0..n T(n, k) | A001003 | 1 1 3 11 45 197 903 4279 20793 103049 518859 2646723 13648869 71039373 372693519 1968801519 |
| Rev | EvenSum∑ k=0..n T(n, k) even(k) | A227506 | 1 1 1 7 17 121 353 2591 8257 61921 207905 1582791 5501073 42344121 150827073 1170747519 4247388417 |
| Rev | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 0 2 4 28 76 550 1688 12536 41128 310954 1063932 8147796 28695252 221866446 798054000 6216189936 |
| Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A001003 | 1 1 -1 3 -11 45 -197 903 -4279 20793 -103049 518859 -2646723 13648869 -71039373 372693519 |
| Rev | AbsSum∑ k=0..n | T(n, k) | | A001003 | 1 1 3 11 45 197 903 4279 20793 103049 518859 2646723 13648869 71039373 372693519 1968801519 |
| Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | A026003 | 1 1 1 3 5 13 25 63 129 321 681 1683 3653 8989 19825 48639 108545 265729 598417 1462563 3317445 |
| Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A010683 | 1 2 7 28 121 550 2591 12536 61921 310954 1582791 8147796 42344121 221866446 1170747519 6216189936 |
| Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 1 5 27 149 829 4633 25975 146009 822585 4643517 26259603 148740045 843724149 4792348785 |
| Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 2 12 528 6120 65577360 2384317320 307331984910720 10705170228466855130640 |
| Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | A055642 | 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 |
| Rev | RowMaxMax k=0..n | T(n, k) | | A006318 | 1 1 2 6 22 90 394 1806 8558 41586 206098 1037718 5293446 27297738 142078746 745387038 3937603038 |
| Rev | ColMiddleT(n, n // 2) | missing | 1 1 2 4 16 30 146 264 1408 2490 14002 24396 142000 244790 1459810 2496528 15158272 25763058 |
| Rev | CentralET(2 n, n) | A103885 | 1 2 16 146 1408 14002 142000 1459810 15158272 158611106 1669752016 17664712562 187641279616 |
| Rev | CentralOT(2 n + 1, n) | A330801 | 1 4 30 264 2490 24396 244790 2496528 25763058 268243860 2812481870 29653804824 314097641130 |
| 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) | A000007 | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| Rev | BinConv∑ k=0..n C(n, k) T(n, k) | A178792 | 1 1 5 31 209 1471 10625 78079 580865 4361215 32978945 250806271 1916280833 14698053631 113104519169 |
| Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A000225 | 1 -1 -3 -7 -15 -31 -63 -127 -255 -511 -1023 -2047 -4095 -8191 -16383 -32767 -65535 -131071 -262143 |
| Rev | TransNat0∑ k=0..n T(n, k) k | missing | 0 0 2 16 104 632 3730 21696 125216 719536 4124658 23612880 135091176 772684776 4419655266 |
| Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 1 5 27 149 829 4633 25975 146009 822585 4643517 26259603 148740045 843724149 4792348785 |
| Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 0 2 28 268 2180 16230 114408 777560 5149752 33461610 214276260 1356538788 8509510620 52981004622 |
| Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A109980 | 1 2 8 36 172 852 4324 22332 116876 618084 3296308 17702412 95627580 519170004 2830862532 |
| Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 -2 0 -4 -12 -52 -228 -1052 -5004 -24388 -121140 -611052 -3121596 -16117428 -83974212 -440941884 |
| Rev | DiagRow1T(n + 1, n) | A006318 | 1 2 6 22 90 394 1806 8558 41586 206098 1037718 5293446 27297738 142078746 745387038 3937603038 |
| Rev | DiagRow2T(n + 2, n) | A006319 | 1 4 16 68 304 1412 6752 33028 164512 831620 4255728 22004292 114781008 603308292 3192216000 |
| Rev | DiagRow3T(n + 3, n) | A006320 | 1 6 30 146 714 3534 17718 89898 461010 2386390 12455118 65478978 346448538 1843520670 9859734630 |
| Rev | DiagCol1T(n + 1, 1) | A005843 | 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 |
| Rev | DiagCol2T(n + 2, 2) | A054000 | 0 6 16 30 48 70 96 126 160 198 240 286 336 390 448 510 576 646 720 798 880 966 1056 1150 1248 1350 |
| Rev | DiagCol3T(n + 3, 3) | missing | 0 22 68 146 264 430 652 938 1296 1734 2260 2882 3608 4446 5404 6490 7712 9078 10596 12274 14120 |
| Rev | Polysee docs | missing | 1 1 1 1 1 1 1 3 1 1 1 11 5 1 1 1 45 33 7 1 1 1 197 253 67 9 1 1 1 903 2121 757 113 11 1 1 1 4279 |
| 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 | A005408 | 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 |
| Rev | PolyRow3∑ k=0..3 T(3, k) n^k | A080859 | 1 11 33 67 113 171 241 323 417 523 641 771 913 1067 1233 1411 1601 1803 2017 2243 2481 2731 2993 |
| Rev | PolyCol2∑ k=0..n T(n, k) 2^k | A330802 | 1 1 5 33 253 2121 18853 174609 1667021 16290969 162171445 1638732129 16765758429 173325794409 |
| Rev | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 1 7 67 757 9421 124771 1725319 24623881 360020857 5364898687 81184517899 1244208082045 |
| Rev | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 1 5 67 1689 65541 3491053 238013959 19839218801 1957984585993 223488773954181 28979637885896523 |
| Inv | RevInvT-1(n, n - k), 0 ≤ k ≤ n | A106579 | 1 1 0 1 2 0 1 4 6 0 1 6 16 22 0 1 8 30 68 90 0 1 10 48 146 304 394 0 1 12 70 264 714 1412 1806 0 1 |
| Inv | Accsee docs | missing | 1 0 1 0 -2 -1 0 2 -2 -1 0 -2 6 0 1 0 2 -10 8 0 1 0 -2 14 -24 8 -2 -1 0 2 -18 48 -40 10 -2 -1 0 -2 |
| Inv | AccRevsee docs | missing | 1 1 1 1 -1 -1 1 -3 -1 -1 1 -5 3 1 1 1 -7 11 -1 1 1 1 -9 23 -15 1 -1 -1 1 -11 39 -49 17 -3 -1 -1 1 |
| Inv | AntiDiagsee docs | missing | 1 0 0 1 0 -2 0 2 1 0 -2 -4 0 2 8 1 0 -2 -12 -6 0 2 16 18 1 0 -2 -20 -38 -8 0 2 24 66 32 1 0 -2 -28 |
| Inv | Diffx1T(n, k) (k+1) | missing | 1 0 2 0 -4 3 0 4 -12 4 0 -4 24 -24 5 0 4 -36 72 -40 6 0 -4 48 -152 160 -60 7 0 4 -60 264 -440 300 |
| Inv | EvenSum∑ k=0..n T(n, k) even(k) | A111587 | 1 0 1 -4 9 -20 49 -120 289 -696 1681 -4060 9801 -23660 57121 -137904 332929 -803760 1940449 |
| Inv | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 1 -2 3 -8 21 -50 119 -288 697 -1682 4059 -9800 23661 -57122 137903 -332928 803761 -1940450 |
| Inv | AltSum∑ k=0..n T(n, k) (-1)^k | A001333 | 1 -1 3 -7 17 -41 99 -239 577 -1393 3363 -8119 19601 -47321 114243 -275807 665857 -1607521 3880899 |
| Inv | AbsSum∑ k=0..n | T(n, k) | | A001333 | 1 1 3 7 17 41 99 239 577 1393 3363 8119 19601 47321 114243 275807 665857 1607521 3880899 9369319 |
| Inv | DiagSum∑ k=0..n // 2 T(n - k, k) | A001590 | 1 0 1 -2 3 -6 11 -20 37 -68 125 -230 423 -778 1431 -2632 4841 -8904 16377 -30122 55403 -101902 |
| Inv | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A093178 | 1 1 -3 -1 5 1 -7 -1 9 1 -11 -1 13 1 -15 -1 17 1 -19 -1 21 1 -23 -1 25 1 -27 -1 29 1 -31 -1 33 1 -35 |
| Inv | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A124625 | 1 2 -1 -4 1 6 -1 -8 1 10 -1 -12 1 14 -1 -16 1 18 -1 -20 1 22 -1 -24 1 26 -1 -28 1 30 -1 -32 1 34 -1 |
| Inv | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 2 4 24 72 3040 6600 342720 12877200 281457792 45725102640 56738793619200 1803731322088080 |
| Inv | RowGcdGcd k=0..n | T(n, k) | > 1 | A055642 | 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 |
| Inv | RowMaxMax k=0..n | T(n, k) | | A110110 | 1 1 2 4 8 18 38 88 192 450 1002 2364 5336 12642 28814 68464 157184 374274 864146 2060980 4780008 |
| Inv | ColMiddleT(n, n // 2) | missing | 1 0 -2 2 8 -12 -38 66 192 -360 -1002 1970 5336 -10836 -28814 59906 157184 -332688 -864146 1854882 |
| Inv | CentralET(2 n, n) | A002003 | 1 -2 8 -38 192 -1002 5336 -28814 157184 -864146 4780008 -26572086 148321344 -830764794 4666890936 |
| Inv | CentralOT(2 n + 1, n) | missing | 0 2 -12 66 -360 1970 -10836 59906 -332688 1854882 -10377180 58227906 -327572856 1847023698 |
| Inv | ColLeftT(n, 0) | 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 | 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 -3 -5 17 31 -111 -209 769 1471 -5503 -10625 40193 78079 -297727 -580865 2228225 4361215 |
| Inv | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A240688 | 1 1 5 19 81 351 1553 6959 31489 143551 658305 3033471 14034177 65147135 303285505 1415422719 |
| Inv | TransNat0∑ k=0..n T(n, k) k | A193356 | 0 1 0 -3 0 5 0 -7 0 9 0 -11 0 13 0 -15 0 17 0 -19 0 21 0 -23 0 25 0 -27 0 29 0 -31 0 33 0 -35 0 37 |
| Inv | TransNat1∑ k=0..n T(n, k) (k + 1) | A124625 | 1 2 -1 -4 1 6 -1 -8 1 10 -1 -12 1 14 -1 -16 1 18 -1 -20 1 22 -1 -24 1 26 -1 -28 1 30 -1 -32 1 34 -1 |
| Inv | TransSqrs∑ k=0..n T(n, k) k^2 | A000982 | 0 1 2 -5 -8 13 18 -25 -32 41 50 -61 -72 85 98 -113 -128 145 162 -181 -200 221 242 -265 -288 313 338 |
| Inv | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A077020 | 1 1 -3 1 5 -7 -3 17 -11 -23 45 1 -91 89 93 -271 85 457 -627 -287 1541 -967 -2115 4049 181 -8279 |
| Inv | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A007483 | 1 1 5 17 61 217 773 2753 9805 34921 124373 442961 1577629 5618809 20011685 71272673 253841389 |
| Inv | DiagRow1T(n + 1, n) | A005843 | 0 -2 -4 -6 -8 -10 -12 -14 -16 -18 -20 -22 -24 -26 -28 -30 -32 -34 -36 -38 -40 -42 -44 -46 -48 -50 |
| Inv | DiagRow2T(n + 2, n) | A001105 | 0 2 8 18 32 50 72 98 128 162 200 242 288 338 392 450 512 578 648 722 800 882 968 1058 1152 1250 |
| Inv | DiagRow3T(n + 3, n) | A035597 | 0 -2 -12 -38 -88 -170 -292 -462 -688 -978 -1340 -1782 -2312 -2938 -3668 -4510 -5472 -6562 -7788 |
| Inv | DiagCol1T(n + 1, 1) | A055642 | 1 -2 2 -2 2 -2 2 -2 2 -2 2 -2 2 -2 2 -2 2 -2 2 -2 2 -2 2 -2 2 -2 2 -2 2 -2 2 -2 2 -2 2 -2 2 -2 2 -2 |
| Inv | DiagCol2T(n + 2, 2) | A008586 | 1 -4 8 -12 16 -20 24 -28 32 -36 40 -44 48 -52 56 -60 64 -68 72 -76 80 -84 88 -92 96 -100 104 -108 |
| Inv | DiagCol3T(n + 3, 3) | A005899 | 1 -6 18 -38 66 -102 146 -198 258 -326 402 -486 578 -678 786 -902 1026 -1158 1298 -1446 1602 -1766 |
| Inv | Polysee docs | missing | 1 0 1 0 1 1 0 -1 2 1 0 -1 0 3 1 0 1 -4 3 4 1 0 1 -4 -3 8 5 1 0 -1 4 -15 8 15 6 1 0 -1 12 -21 -8 35 |
| 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 | 0 -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 | missing | 0 -1 -4 -3 8 35 84 161 272 423 620 869 1176 1547 1988 2505 3104 3791 4572 5453 6440 7539 8756 10097 |
| Inv | PolyCol2∑ k=0..n T(n, k) 2^k | A078050 | 1 2 0 -4 -4 4 12 4 -20 -28 12 68 44 -92 -180 4 364 356 -372 -1084 -340 1828 2508 -1148 -6164 -3868 |
| Inv | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 3 3 -3 -15 -21 3 69 129 51 -285 -723 -591 987 3747 4533 -2175 -17949 -29373 -4899 78321 171339 |
| Inv | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 1 0 -3 -8 85 2724 62489 1456624 36537417 997685180 29653122389 955955086824 33278514154717 |
| Inv:Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A122538 | 1 0 1 0 2 1 0 6 4 1 0 22 16 6 1 0 90 68 30 8 1 0 394 304 146 48 10 1 0 1806 1412 714 264 70 12 1 0 |
| Inv:Rev | Accsee docs | missing | 1 1 1 1 -1 -1 1 -3 -1 -1 1 -5 3 1 1 1 -7 11 -1 1 1 1 -9 23 -15 1 -1 -1 1 -11 39 -49 17 -3 -1 -1 1 |
| Inv:Rev | AccRevsee docs | missing | 1 0 1 0 -2 -1 0 2 -2 -1 0 -2 6 0 1 0 2 -10 8 0 1 0 -2 14 -24 8 -2 -1 0 2 -18 48 -40 10 -2 -1 0 -2 |
| Inv:Rev | AntiDiagsee docs | missing | 1 1 1 0 1 -2 1 -4 0 1 -6 2 1 -8 8 0 1 -10 18 -2 1 -12 32 -12 0 1 -14 50 -38 2 1 -16 72 -88 16 0 1 |
| Inv:Rev | Diffx1T(n, k) (k+1) | missing | 1 1 0 1 -4 0 1 -8 6 0 1 -12 24 -8 0 1 -16 54 -48 10 0 1 -20 96 -152 80 -12 0 1 -24 150 -352 330 |
| Inv:Rev | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 1 1 3 9 21 49 119 289 697 1681 4059 9801 23661 57121 137903 332929 803761 1940449 4684659 |
| Inv:Rev | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 0 -2 -4 -8 -20 -50 -120 -288 -696 -1682 -4060 -9800 -23660 -57122 -137904 -332928 -803760 |
| Inv:Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A001333 | 1 1 3 7 17 41 99 239 577 1393 3363 8119 19601 47321 114243 275807 665857 1607521 3880899 9369319 |
| Inv:Rev | AbsSum∑ k=0..n | T(n, k) | | A001333 | 1 1 3 7 17 41 99 239 577 1393 3363 8119 19601 47321 114243 275807 665857 1607521 3880899 9369319 |
| Inv:Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | A180735 | 1 1 1 -1 -3 -3 1 7 9 1 -15 -25 -11 29 65 47 -47 -159 -159 47 365 477 65 -777 -1319 -607 1489 3415 |
| Inv:Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A124625 | 1 2 -1 -4 1 6 -1 -8 1 10 -1 -12 1 14 -1 -16 1 18 -1 -20 1 22 -1 -24 1 26 -1 -28 1 30 -1 -32 1 34 -1 |
| Inv:Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A093178 | 1 1 -3 -1 5 1 -7 -1 9 1 -11 -1 13 1 -15 -1 17 1 -19 -1 21 1 -23 -1 25 1 -27 -1 29 1 -31 -1 33 1 -35 |
| Inv:Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 2 4 24 72 3040 6600 342720 12877200 281457792 45725102640 56738793619200 1803731322088080 |
| Inv:Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | A055642 | 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 |
| Inv:Rev | RowMaxMax k=0..n | T(n, k) | | A110110 | 1 1 2 4 8 18 38 88 192 450 1002 2364 5336 12642 28814 68464 157184 374274 864146 2060980 4780008 |
| Inv:Rev | ColMiddleT(n, n // 2) | A110110 | 1 1 -2 -4 8 18 -38 -88 192 450 -1002 -2364 5336 12642 -28814 -68464 157184 374274 -864146 -2060980 |
| Inv:Rev | CentralET(2 n, n) | A002003 | 1 -2 8 -38 192 -1002 5336 -28814 157184 -864146 4780008 -26572086 148321344 -830764794 4666890936 |
| Inv:Rev | CentralOT(2 n + 1, n) | A050146 | 1 -4 18 -88 450 -2364 12642 -68464 374274 -2060980 11414898 -63521352 354870594 -1989102444 |
| 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) | 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 | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 1 -3 -5 17 31 -111 -209 769 1471 -5503 -10625 40193 78079 -297727 -580865 2228225 4361215 |
| Inv:Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A240688 | 1 -1 5 -19 81 -351 1553 -6959 31489 -143551 658305 -3033471 14034177 -65147135 303285505 |
| Inv:Rev | TransNat0∑ k=0..n T(n, k) k | A237420 | 0 0 -2 0 4 0 -6 0 8 0 -10 0 12 0 -14 0 16 0 -18 0 20 0 -22 0 24 0 -26 0 28 0 -30 0 32 0 -34 0 36 0 |
| Inv:Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | A093178 | 1 1 -3 -1 5 1 -7 -1 9 1 -11 -1 13 1 -15 -1 17 1 -19 -1 21 1 -23 -1 25 1 -27 -1 29 1 -31 -1 33 1 -35 |
| Inv:Rev | TransSqrs∑ k=0..n T(n, k) k^2 | A007590 | 0 0 -2 4 8 -12 -18 24 32 -40 -50 60 72 -84 -98 112 128 -144 -162 180 200 -220 -242 264 288 -312 |
| Inv:Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A078050 | 1 2 0 -4 -4 4 12 4 -20 -28 12 68 44 -92 -180 4 364 356 -372 -1084 -340 1828 2508 -1148 -6164 -3868 |
| Inv:Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A104934 | 1 -2 8 -28 100 -356 1268 -4516 16084 -57284 204020 -726628 2587924 -9217028 32826932 -116914852 |
| Inv:Rev | DiagRow1T(n + 1, n) | A055642 | 1 -2 2 -2 2 -2 2 -2 2 -2 2 -2 2 -2 2 -2 2 -2 2 -2 2 -2 2 -2 2 -2 2 -2 2 -2 2 -2 2 -2 2 -2 2 -2 2 -2 |
| Inv:Rev | DiagRow2T(n + 2, n) | A008586 | 1 -4 8 -12 16 -20 24 -28 32 -36 40 -44 48 -52 56 -60 64 -68 72 -76 80 -84 88 -92 96 -100 104 -108 |
| Inv:Rev | DiagRow3T(n + 3, n) | A005899 | 1 -6 18 -38 66 -102 146 -198 258 -326 402 -486 578 -678 786 -902 1026 -1158 1298 -1446 1602 -1766 |
| Inv:Rev | DiagCol1T(n + 1, 1) | A005843 | 0 -2 -4 -6 -8 -10 -12 -14 -16 -18 -20 -22 -24 -26 -28 -30 -32 -34 -36 -38 -40 -42 -44 -46 -48 -50 |
| Inv:Rev | DiagCol2T(n + 2, 2) | A001105 | 0 2 8 18 32 50 72 98 128 162 200 242 288 338 392 450 512 578 648 722 800 882 968 1058 1152 1250 |
| Inv:Rev | DiagCol3T(n + 3, 3) | A035597 | 0 -2 -12 -38 -88 -170 -292 -462 -688 -978 -1340 -1782 -2312 -2938 -3668 -4510 -5472 -6562 -7788 |
| Inv:Rev | Polysee docs | missing | 1 1 1 1 1 1 1 -1 1 1 1 -1 -3 1 1 1 1 1 -5 1 1 1 1 5 7 -7 1 1 1 -1 -7 1 17 -9 1 1 1 -1 -3 -23 -23 31 |
| 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 | A005408 | 1 -1 -3 -5 -7 -9 -11 -13 -15 -17 -19 -21 -23 -25 -27 -29 -31 -33 -35 -37 -39 -41 -43 -45 -47 -49 |
| Inv:Rev | PolyRow3∑ k=0..3 T(3, k) n^k | A056220 | 1 -1 1 7 17 31 49 71 97 127 161 199 241 287 337 391 449 511 577 647 721 799 881 967 1057 1151 1249 |
| Inv:Rev | PolyCol2∑ k=0..n T(n, k) 2^k | A077020 | 1 1 -3 1 5 -7 -3 17 -11 -23 45 1 -91 89 93 -271 85 457 -627 -287 1541 -967 -2115 4049 181 -8279 |
| Inv:Rev | PolyCol3∑ k=0..n T(n, k) 3^k | A087455 | 1 1 -5 7 1 -23 43 -17 -95 241 -197 -329 1249 -1511 -725 5983 -9791 1633 26107 -57113 35905 99529 |
| Inv:Rev | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 1 -3 7 -23 161 -1931 29807 -541295 11250433 -263529379 6874282999 -197722407431 6218421457249 |
| << | 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.