OEIS Similars: A354794, A039621
| ↕ Type | ↕ Trait | ↕ Anum | ↕ Sequence |
|---|---|---|---|
| Std | TriangleT(n, k), 0 ≤ k ≤ n | A354794 | 1 0 1 0 1 1 0 4 3 1 0 27 19 6 1 0 256 175 55 10 1 0 3125 2101 660 125 15 1 0 46656 31031 9751 1890 |
| Std | RevT(n, n - k), 0 ≤ k ≤ n | missing | 1 1 0 1 1 0 1 3 4 0 1 6 19 27 0 1 10 55 175 256 0 1 15 125 660 2101 3125 0 1 21 245 1890 9751 31031 |
| Std | InvT-1(n, k), 0 ≤ k ≤ n | A354795 | 1 0 1 0 -1 1 0 -1 -3 1 0 -2 -1 -6 1 0 -6 0 5 -10 1 0 -24 4 15 25 -15 1 0 -120 28 49 35 70 -21 1 0 |
| Std | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 0 1 -1 0 1 -3 -1 0 1 -6 -1 -2 0 1 -10 5 0 -6 0 1 -15 25 15 4 -24 0 1 -21 70 35 49 28 -120 0 1 |
| Std | Accsee docs | missing | 1 0 1 0 1 2 0 4 7 8 0 27 46 52 53 0 256 431 486 496 497 0 3125 5226 5886 6011 6026 6027 0 46656 |
| Std | AccRevsee docs | missing | 1 1 1 1 2 2 1 4 8 8 1 7 26 53 53 1 11 66 241 497 497 1 16 141 801 2902 6027 6027 1 22 267 2157 |
| Std | AntiDiagsee docs | missing | 1 0 0 1 0 1 0 4 1 0 27 3 0 256 19 1 0 3125 175 6 0 46656 2101 55 1 0 823543 31031 660 10 0 16777216 |
| Std | Diffx1T(n, k) (k+1) | missing | 1 0 2 0 2 3 0 8 9 4 0 54 57 24 5 0 512 525 220 50 6 0 6250 6303 2640 625 90 7 0 93312 93093 39004 |
| Std | RowSum∑ k=0..n T(n, k) | A195979 | 1 1 2 8 53 497 6027 89595 1576682 32047986 738772383 19042778713 542704904381 16944005908637 |
| Std | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 0 1 3 20 185 2227 32942 577663 11710659 269400564 6932743719 197313157857 6153519636992 |
| Std | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 1 1 5 33 312 3800 56653 999019 20337327 469371819 12110034994 345391746524 10790486271645 |
| Std | AltSum∑ k=0..n T(n, k) (-1)^k | A290219 | 1 -1 0 -2 -13 -127 -1573 -23711 -421356 -8626668 -199971255 -5177291275 -148078588667 |
| Std | AbsSum∑ k=0..n | T(n, k) | | A195979 | 1 1 2 8 53 497 6027 89595 1576682 32047986 738772383 19042778713 542704904381 16944005908637 |
| Std | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 0 1 1 5 30 276 3306 48813 855244 17330700 398605707 10256700243 291905248607 9103478259999 |
| Std | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 1 3 19 178 2166 32301 569871 11606645 267990533 6916941980 197344729110 6167098677301 |
| Std | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 2 5 21 140 1313 15915 236484 4160175 84537313 1948326616 50211394159 1430769984033 44664919048610 |
| Std | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 1 12 1026 492800 78787500 10083803970240 27122723143943517881700 |
| Std | RowGcdGcd k=0..n | T(n, k) | > 1 | 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 | RowMaxMax k=0..n | T(n, k) | | A000312 | 1 1 1 4 27 256 3125 46656 823543 16777216 387420489 10000000000 285311670611 8916100448256 |
| Std | ColMiddleT(n, n // 2) | missing | 1 0 1 4 19 175 660 9751 33621 688506 2263065 59411605 189556312 6078494136 19004025040 720369582933 |
| Std | CentralET(2 n, n) | missing | 1 1 19 660 33621 2263065 189556312 19004025040 2219237925333 295863079545891 44341076439851555 |
| Std | CentralOT(2 n + 1, n) | missing | 0 4 175 9751 688506 59411605 6078494136 720369582933 97118267918100 14683524204220950 |
| 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) | missing | 1 1 3 22 247 3631 65431 1390971 34000275 938046703 28802563636 973403048586 35885630672233 |
| Std | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 1 -1 4 -17 31 1351 -44925 1172963 -29981273 788395396 -21624745614 619619507497 -18464045211403 |
| Std | TransNat0∑ k=0..n T(n, k) k | missing | 0 1 3 13 87 816 9888 146889 2583493 52489327 1209554233 31168615446 888065079652 27720913139973 |
| Std | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 2 5 21 140 1313 15915 236484 4160175 84537313 1948326616 50211394159 1430769984033 44664919048610 |
| Std | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 5 25 173 1636 19880 295709 5204799 105796675 2438745735 62857944414 1791282114924 |
| Std | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 1 3 23 305 5737 139427 4151135 146249217 5949873009 274474594467 14156477873287 807206849914225 |
| Std | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 1 -1 11 -151 2897 -71193 2134827 -75588175 3086475009 -142784470929 7380788246251 |
| Std | DiagRow1T(n + 1, n) | A000217 | 0 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 |
| Std | DiagRow2T(n + 2, n) | A215862 | 0 4 19 55 125 245 434 714 1110 1650 2365 3289 4459 5915 7700 9860 12444 15504 19095 23275 28105 |
| Std | DiagRow3T(n + 3, n) | missing | 0 27 175 660 1890 4550 9702 18900 34320 58905 96525 152152 232050 343980 497420 703800 976752 |
| Std | DiagCol1T(n + 1, 1) | A000312 | 1 1 4 27 256 3125 46656 823543 16777216 387420489 10000000000 285311670611 8916100448256 |
| Std | DiagCol2T(n + 2, 2) | A045531 | 1 3 19 175 2101 31031 543607 11012415 253202761 6513215599 185311670611 5777672071535 |
| Std | DiagCol3T(n + 3, 3) | A281596 | 1 6 55 660 9751 170898 3463615 79669320 2050086511 58346365110 1819621847407 61705703989020 |
| Std | Polysee docs | missing | 1 0 1 0 1 1 0 2 2 1 0 8 6 3 1 0 53 28 12 4 1 0 497 194 66 20 5 1 0 6027 1844 495 128 30 6 1 0 89595 |
| 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 | A002378 | 0 2 6 12 20 30 42 56 72 90 110 132 156 182 210 240 272 306 342 380 420 462 506 552 600 650 702 756 |
| Std | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 0 8 28 66 128 220 348 518 736 1008 1340 1738 2208 2756 3388 4110 4928 5848 6876 8018 9280 10668 |
| Std | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 2 6 28 194 1844 22478 334996 5903850 120116148 2770736934 71453347508 2037107356402 |
| Std | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 3 12 66 495 4881 60603 912645 16190472 330894912 7657986573 197983974909 5655576667605 |
| Std | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 1 6 66 1052 21905 562242 17141481 604952952 24249218922 1088041350990 54018946202573 |
| Alt | TriangleT(n, k), 0 ≤ k ≤ n | A354794 | 1 0 -1 0 -1 1 0 -4 3 -1 0 -27 19 -6 1 0 -256 175 -55 10 -1 0 -3125 2101 -660 125 -15 1 0 -46656 |
| Alt | RevT(n, n - k), 0 ≤ k ≤ n | missing | 1 -1 0 1 -1 0 -1 3 -4 0 1 -6 19 -27 0 -1 10 -55 175 -256 0 1 -15 125 -660 2101 -3125 0 -1 21 -245 |
| Alt | InvT-1(n, k), 0 ≤ k ≤ n | missing | 1 0 1 0 1 1 0 1 -3 1 0 14 -37 6 1 0 -4 30 -5 -10 1 0 -126 994 -165 -275 15 1 0 582 -3878 651 1435 |
| Alt | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 0 1 1 0 1 -3 1 0 1 6 -37 14 0 1 -10 -5 30 -4 0 1 15 -275 -165 994 -126 0 1 -21 -70 1435 651 |
| Alt | Accsee docs | missing | 1 0 -1 0 -1 0 0 -4 -1 -2 0 -27 -8 -14 -13 0 -256 -81 -136 -126 -127 0 -3125 -1024 -1684 -1559 -1574 |
| Alt | AccRevsee docs | missing | 1 -1 -1 1 0 0 -1 2 -2 -2 1 -5 14 -13 -13 -1 9 -46 129 -127 -127 1 -14 111 -549 1552 -1573 -1573 -1 |
| Alt | AntiDiagsee docs | missing | 1 0 0 -1 0 -1 0 -4 1 0 -27 3 0 -256 19 -1 0 -3125 175 -6 0 -46656 2101 -55 1 0 -823543 31031 -660 |
| Alt | Diffx1T(n, k) (k+1) | missing | 1 0 -2 0 -2 3 0 -8 9 -4 0 -54 57 -24 5 0 -512 525 -220 50 -6 0 -6250 6303 -2640 625 -90 7 0 -93312 |
| Alt | RowSum∑ k=0..n T(n, k) | A290219 | 1 -1 0 -2 -13 -127 -1573 -23711 -421356 -8626668 -199971255 -5177291275 -148078588667 |
| Alt | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 0 1 3 20 185 2227 32942 577663 11710659 269400564 6932743719 197313157857 6153519636992 |
| Alt | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 -1 -1 -5 -33 -312 -3800 -56653 -999019 -20337327 -469371819 -12110034994 -345391746524 |
| Alt | AltSum∑ k=0..n T(n, k) (-1)^k | A195979 | 1 1 2 8 53 497 6027 89595 1576682 32047986 738772383 19042778713 542704904381 16944005908637 |
| Alt | AbsSum∑ k=0..n | T(n, k) | | A195979 | 1 1 2 8 53 497 6027 89595 1576682 32047986 738772383 19042778713 542704904381 16944005908637 |
| Alt | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 0 -1 -1 -3 -24 -238 -2956 -44609 -793162 -16243236 -376577097 -9750227477 -278877440355 |
| Alt | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 -1 -1 -7 -62 -726 -10539 -182295 -3657331 -83452061 -2133485080 -60393952730 -1874982282491 |
| Alt | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 -2 1 -3 -16 -163 -2045 -31104 -556229 -11441287 -266169980 -6910833845 -198117958847 |
| Alt | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 1 12 1026 492800 78787500 10083803970240 27122723143943517881700 |
| Alt | RowGcdGcd k=0..n | T(n, k) | > 1 | 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 | RowMaxMax k=0..n | T(n, k) | | A000312 | 1 1 1 4 27 256 3125 46656 823543 16777216 387420489 10000000000 285311670611 8916100448256 |
| Alt | ColMiddleT(n, n // 2) | missing | 1 0 -1 -4 19 175 -660 -9751 33621 688506 -2263065 -59411605 189556312 6078494136 -19004025040 |
| Alt | CentralET(2 n, n) | missing | 1 -1 19 -660 33621 -2263065 189556312 -19004025040 2219237925333 -295863079545891 44341076439851555 |
| Alt | CentralOT(2 n + 1, n) | missing | 0 -4 175 -9751 688506 -59411605 6078494136 -720369582933 97118267918100 -14683524204220950 |
| 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) | missing | 1 -1 -1 -4 -17 -31 1351 44925 1172963 29981273 788395396 21624745614 619619507497 18464045211403 |
| Alt | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -1 3 -22 247 -3631 65431 -1390971 34000275 -938046703 28802563636 -973403048586 35885630672233 |
| Alt | TransNat0∑ k=0..n T(n, k) k | missing | 0 -1 1 -1 -3 -36 -472 -7393 -134873 -2814619 -66198725 -1733542570 -50039370180 -1578825105157 |
| Alt | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 -2 1 -3 -16 -163 -2045 -31104 -556229 -11441287 -266169980 -6910833845 -198117958847 |
| Alt | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 -1 3 -1 11 84 1000 14531 251305 5037989 114844257 2933087178 82947996884 2572839049299 |
| Alt | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 -1 -1 -11 -151 -2897 -71193 -2134827 -75588175 -3086475009 -142784470929 -7380788246251 |
| Alt | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 -1 3 -23 305 -5737 139427 -4151135 146249217 -5949873009 274474594467 -14156477873287 |
| Alt | DiagRow1T(n + 1, n) | A000217 | 0 -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 | DiagRow2T(n + 2, n) | A215862 | 0 -4 19 -55 125 -245 434 -714 1110 -1650 2365 -3289 4459 -5915 7700 -9860 12444 -15504 19095 -23275 |
| Alt | DiagRow3T(n + 3, n) | missing | 0 -27 175 -660 1890 -4550 9702 -18900 34320 -58905 96525 -152152 232050 -343980 497420 -703800 |
| Alt | DiagCol1T(n + 1, 1) | A000312 | -1 -1 -4 -27 -256 -3125 -46656 -823543 -16777216 -387420489 -10000000000 -285311670611 |
| Alt | DiagCol2T(n + 2, 2) | A045531 | 1 3 19 175 2101 31031 543607 11012415 253202761 6513215599 185311670611 5777672071535 |
| Alt | DiagCol3T(n + 3, 3) | A281596 | -1 -6 -55 -660 -9751 -170898 -3463615 -79669320 -2050086511 -58346365110 -1819621847407 |
| Alt | Polysee docs | missing | 1 0 1 0 -1 1 0 0 -2 1 0 -2 2 -3 1 0 -13 -4 6 -4 1 0 -127 -10 -12 12 -5 1 0 -1573 -124 9 -32 20 -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 | A002378 | 0 0 2 6 12 20 30 42 56 72 90 110 132 156 182 210 240 272 306 342 380 420 462 506 552 600 650 702 |
| Alt | PolyRow3∑ k=0..3 T(3, k) n^k | A242659 | 0 -2 -4 -12 -32 -70 -132 -224 -352 -522 -740 -1012 -1344 -1742 -2212 -2760 -3392 -4114 -4932 -5852 |
| Alt | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 -2 2 -4 -10 -124 -1542 -23580 -423058 -8724348 -203374782 -5289091196 -151831692730 |
| Alt | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 -3 6 -12 9 -111 -1077 -17289 -313050 -6515562 -152969301 -4001127807 -115402527123 -3639124229175 |
| Alt | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 -1 2 -12 68 -655 6342 -83405 1147400 -19186884 341301210 -6951750575 151260026700 -3641972785945 |
| Rev | TriangleT(n, k), 0 ≤ k ≤ n | missing | 1 1 0 1 1 0 1 3 4 0 1 6 19 27 0 1 10 55 175 256 0 1 15 125 660 2101 3125 0 1 21 245 1890 9751 31031 |
| Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A354795 | 1 0 1 0 -1 1 0 -1 -3 1 0 -2 -1 -6 1 0 -6 0 5 -10 1 0 -24 4 15 25 -15 1 0 -120 28 49 35 70 -21 1 0 |
| Rev | Accsee docs | missing | 1 1 1 1 2 2 1 4 8 8 1 7 26 53 53 1 11 66 241 497 497 1 16 141 801 2902 6027 6027 1 22 267 2157 |
| Rev | AccRevsee docs | missing | 1 0 1 0 1 2 0 4 7 8 0 27 46 52 53 0 256 431 486 496 497 0 3125 5226 5886 6011 6026 6027 0 46656 |
| Rev | AntiDiagsee docs | missing | 1 1 1 0 1 1 1 3 0 1 6 4 1 10 19 0 1 15 55 27 1 21 125 175 0 1 28 245 660 256 1 36 434 1890 2101 0 1 |
| Rev | Diffx1T(n, k) (k+1) | missing | 1 1 0 1 2 0 1 6 12 0 1 12 57 108 0 1 20 165 700 1280 0 1 30 375 2640 10505 18750 0 1 42 735 7560 |
| Rev | RowSum∑ k=0..n T(n, k) | A195979 | 1 1 2 8 53 497 6027 89595 1576682 32047986 738772383 19042778713 542704904381 16944005908637 |
| Rev | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 1 1 5 20 312 2227 56653 577663 20337327 269400564 12110034994 197313157857 10790486271645 |
| Rev | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 0 1 3 33 185 3800 32942 999019 11710659 469371819 6932743719 345391746524 6153519636992 |
| Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A290219 | 1 1 0 2 -13 127 -1573 23711 -421356 8626668 -199971255 5177291275 -148078588667 4636966634653 |
| Rev | AbsSum∑ k=0..n | T(n, k) | | A195979 | 1 1 2 8 53 497 6027 89595 1576682 32047986 738772383 19042778713 542704904381 16944005908637 |
| Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 1 2 4 11 30 98 322 1190 4462 18186 75520 333952 1507164 7147736 34608912 174505668 898042208 |
| Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 2 5 21 140 1313 15915 236484 4160175 84537313 1948326616 50211394159 1430769984033 44664919048610 |
| Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 1 3 19 178 2166 32301 569871 11606645 267990533 6916941980 197344729110 6167098677301 |
| Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 1 12 1026 492800 78787500 10083803970240 27122723143943517881700 |
| Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | 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 | RowMaxMax k=0..n | T(n, k) | | A000312 | 1 1 1 4 27 256 3125 46656 823543 16777216 387420489 10000000000 285311670611 8916100448256 |
| Rev | ColMiddleT(n, n // 2) | missing | 1 1 1 3 19 55 660 1890 33621 95781 2263065 6427575 189556312 537306484 19004025040 53791898160 |
| Rev | CentralET(2 n, n) | missing | 1 1 19 660 33621 2263065 189556312 19004025040 2219237925333 295863079545891 44341076439851555 |
| Rev | CentralOT(2 n + 1, n) | missing | 1 3 55 1890 95781 6427575 537306484 53791898160 6275077781973 835898091070185 125195263380478655 |
| 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) | missing | 1 1 3 22 247 3631 65431 1390971 34000275 938046703 28802563636 973403048586 35885630672233 |
| Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -1 -1 -4 -17 -31 1351 44925 1172963 29981273 788395396 21624745614 619619507497 18464045211403 |
| Rev | TransNat0∑ k=0..n T(n, k) k | missing | 0 0 1 11 125 1669 26274 480276 10029963 235942547 6178169597 178301950397 5624393772920 |
| Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 1 3 19 178 2166 32301 569871 11606645 267990533 6916941980 197344729110 6167098677301 |
| Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 0 1 19 325 5901 118196 2629418 64776559 1756875655 52124899375 1681324628875 58627226434140 |
| Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 2 6 28 194 1844 22478 334996 5903850 120116148 2770736934 71453347508 2037107356402 |
| Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 -2 2 -4 -10 -124 -1542 -23580 -423058 -8724348 -203374782 -5289091196 -151831692730 |
| Rev | DiagRow1T(n + 1, n) | A000312 | 1 1 4 27 256 3125 46656 823543 16777216 387420489 10000000000 285311670611 8916100448256 |
| Rev | DiagRow2T(n + 2, n) | A045531 | 1 3 19 175 2101 31031 543607 11012415 253202761 6513215599 185311670611 5777672071535 |
| Rev | DiagRow3T(n + 3, n) | A281596 | 1 6 55 660 9751 170898 3463615 79669320 2050086511 58346365110 1819621847407 61705703989020 |
| Rev | DiagCol1T(n + 1, 1) | A000217 | 0 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 |
| Rev | DiagCol2T(n + 2, 2) | A215862 | 0 4 19 55 125 245 434 714 1110 1650 2365 3289 4459 5915 7700 9860 12444 15504 19095 23275 28105 |
| Rev | DiagCol3T(n + 3, 3) | missing | 0 27 175 660 1890 4550 9702 18900 34320 58905 96525 152152 232050 343980 497420 703800 976752 |
| Rev | Polysee docs | missing | 1 1 1 1 1 1 1 2 1 1 1 8 3 1 1 1 53 23 4 1 1 1 497 305 46 5 1 1 1 6027 5737 919 77 6 1 1 1 89595 |
| 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 | A000027 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 |
| Rev | PolyRow3∑ k=0..3 T(3, k) n^k | A033951 | 1 8 23 46 77 116 163 218 281 352 431 518 613 716 827 946 1073 1208 1351 1502 1661 1828 2003 2186 |
| Rev | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 1 3 23 305 5737 139427 4151135 146249217 5949873009 274474594467 14156477873287 807206849914225 |
| Rev | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 1 4 46 919 25987 948547 42395887 2241756400 136859774824 9473301026461 733088533203391 |
| Rev | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 1 3 46 2057 183301 27170047 6034642335 1875338217825 776758174028938 413553645413381451 |
| Inv | TriangleT(n, k), 0 ≤ k ≤ n | A354795 | 1 0 1 0 -1 1 0 -1 -3 1 0 -2 -1 -6 1 0 -6 0 5 -10 1 0 -24 4 15 25 -15 1 0 -120 28 49 35 70 -21 1 0 |
| Inv | RevT(n, n - k), 0 ≤ k ≤ n | missing | 1 1 0 1 -1 0 1 -3 -1 0 1 -6 -1 -2 0 1 -10 5 0 -6 0 1 -15 25 15 4 -24 0 1 -21 70 35 49 28 -120 0 1 |
| Inv | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 0 1 1 0 1 3 4 0 1 6 19 27 0 1 10 55 175 256 0 1 15 125 660 2101 3125 0 1 21 245 1890 9751 31031 |
| Inv | Accsee docs | missing | 1 0 1 0 -1 0 0 -1 -4 -3 0 -2 -3 -9 -8 0 -6 -6 -1 -11 -10 0 -24 -20 -5 20 5 6 0 -120 -92 -43 -8 62 |
| Inv | AccRevsee docs | missing | 1 1 1 1 0 0 1 -2 -3 -3 1 -5 -6 -8 -8 1 -9 -4 -4 -10 -10 1 -14 11 26 30 6 6 1 -20 50 85 134 162 42 |
| Inv | AntiDiagsee docs | missing | 1 0 0 1 0 -1 0 -1 1 0 -2 -3 0 -6 -1 1 0 -24 0 -6 0 -120 4 5 1 0 -720 28 15 -10 0 -5040 188 49 25 1 |
| Inv | Diffx1T(n, k) (k+1) | missing | 1 0 2 0 -2 3 0 -2 -9 4 0 -4 -3 -24 5 0 -12 0 20 -50 6 0 -48 12 60 125 -90 7 0 -240 84 196 175 420 |
| Inv | RowSum∑ k=0..n T(n, k) | A176118 | 1 1 0 -3 -8 -10 6 42 -160 -2952 -27720 -253440 -2553528 -28562664 -349272000 -4618376280 |
| Inv | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 0 1 -3 0 -10 30 42 392 1080 9720 83160 871992 9522240 112875672 1440913320 19782929280 |
| Inv | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 1 -1 0 -8 0 -24 0 -552 -4032 -37440 -336600 -3425520 -38084904 -462147672 -6059289600 |
| Inv | AltSum∑ k=0..n T(n, k) (-1)^k | A005727 | 1 -1 2 -3 8 -10 54 42 944 5112 47160 419760 4297512 47607144 575023344 7500202920 105180931200 |
| Inv | AbsSum∑ k=0..n | T(n, k) | | missing | 1 1 2 5 10 22 84 324 1336 8166 61454 520940 4999422 53618008 630968324 8068178720 111396089176 |
| Inv | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 0 1 -1 0 -5 -6 -30 -110 -687 -4777 -38736 -350800 -3525273 -38918468 -468386625 -6103700165 |
| Inv | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 1 -1 -8 -22 -34 -18 -118 -2616 -29160 -282960 -2858448 -31603944 -382467864 -5018253576 |
| Inv | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 2 1 -7 -26 -36 66 496 1016 -3312 -49680 -436272 -4145448 -45972096 -570098424 -7658244120 |
| Inv | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 1 3 6 30 600 5880 18239760 435037680 68769684547200 84388489622236800 723633960319757625600 |
| Inv | RowGcdGcd k=0..n | T(n, k) | > 1 | A114890 | 1 1 1 3 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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 | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 1 3 6 10 25 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 |
| Inv | ColMiddleT(n, n // 2) | missing | 1 0 -1 -1 -1 0 15 49 49 0 -1365 -7645 -7645 0 311311 2475473 2475473 0 -132652377 -1367593305 |
| Inv | CentralET(2 n, n) | A298511 | 1 -1 -1 15 49 -1365 -7645 311311 2475473 -132652377 -1367593305 90881245455 1151541572401 |
| Inv | CentralOT(2 n + 1, n) | missing | 0 -1 0 49 0 -7645 0 2475473 0 -1367593305 0 1151541572401 0 -1373222414339685 0 2202549127844351265 |
| 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 -1 -11 -37 -29 502 4012 17999 43171 -93629 -1736965 -10217612 -15805568 470437528 9107848986 |
| Inv | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 1 3 7 27 71 370 680 8015 -12341 372031 -2830563 38292628 -460951568 6421791272 -93716919894 |
| Inv | TransNat0∑ k=0..n T(n, k) k | missing | 0 1 1 -4 -18 -26 60 454 1176 -360 -21960 -182832 -1591920 -17409432 -220826424 -3039867840 |
| Inv | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 2 1 -7 -26 -36 66 496 1016 -3312 -49680 -436272 -4145448 -45972096 -570098424 -7658244120 |
| Inv | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 3 -4 -44 -96 188 2036 6816 6264 -53328 -309024 -603792 2422536 21808824 -94797840 -5753065344 |
| Inv | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 1 -1 -9 -31 -95 -513 -5481 -72511 -1059327 -17258625 -314205705 -6342349407 -140644383711 |
| Inv | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 1 3 3 25 -55 843 -7749 99377 -1405359 22766355 -412221645 8272106313 -182245108071 4374795235419 |
| Inv | DiagRow1T(n + 1, n) | A000217 | 0 -1 -3 -6 -10 -15 -21 -28 -36 -45 -55 -66 -78 -91 -105 -120 -136 -153 -171 -190 -210 -231 -253 |
| Inv | DiagRow2T(n + 2, n) | A059302 | 0 -1 -1 5 25 70 154 294 510 825 1265 1859 2639 3640 4900 6460 8364 10659 13395 16625 20405 24794 |
| Inv | DiagRow3T(n + 3, n) | missing | 0 -2 0 15 35 0 -252 -1050 -2970 -6930 -14300 -27027 -47775 -80080 -128520 -198900 -298452 -436050 |
| Inv | DiagCol1T(n + 1, 1) | A000142 | 1 -1 -1 -2 -6 -24 -120 -720 -5040 -40320 -362880 -3628800 -39916800 -479001600 -6227020800 |
| Inv | DiagCol2T(n + 2, 2) | A045406 | 1 -3 -1 0 4 28 188 1368 11016 98208 964512 10370880 121337280 1535880960 20924455680 305396421120 |
| Inv | DiagCol3T(n + 3, 3) | A347276 | 1 -6 5 15 49 196 944 5340 34716 254760 2078856 18620784 180973584 1887504768 20887922304 |
| Inv | Polysee docs | missing | 1 0 1 0 1 1 0 0 2 1 0 -3 2 3 1 0 -8 -6 6 4 1 0 -10 -40 -3 12 5 1 0 6 -100 -96 12 20 6 1 0 42 72 |
| 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 | A002378 | 0 0 2 6 12 20 30 42 56 72 90 110 132 156 182 210 240 272 306 342 380 420 462 506 552 600 650 702 |
| Inv | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 0 -3 -6 -3 12 45 102 189 312 477 690 957 1284 1677 2142 2685 3312 4029 4842 5757 6780 7917 9174 |
| Inv | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 2 2 -6 -40 -100 72 1848 8192 8352 -139680 -1235520 -6657792 -37195392 -382335744 -5807571840 |
| Inv | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 3 6 -3 -96 -450 -522 7938 66384 209304 -772200 -13899600 -82230552 -114793848 2417497488 |
| Inv | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 1 2 -3 -152 -2530 -34344 -369222 -1265536 97121592 4374338400 129274334640 2899756412928 |
| Inv:Rev | TriangleT(n, k), 0 ≤ k ≤ n | missing | 1 1 0 1 -1 0 1 -3 -1 0 1 -6 -1 -2 0 1 -10 5 0 -6 0 1 -15 25 15 4 -24 0 1 -21 70 35 49 28 -120 0 1 |
| Inv:Rev | RevT(n, n - k), 0 ≤ k ≤ n | A354795 | 1 0 1 0 -1 1 0 -1 -3 1 0 -2 -1 -6 1 0 -6 0 5 -10 1 0 -24 4 15 25 -15 1 0 -120 28 49 35 70 -21 1 0 |
| Inv:Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A354794 | 1 0 1 0 1 1 0 4 3 1 0 27 19 6 1 0 256 175 55 10 1 0 3125 2101 660 125 15 1 0 46656 31031 9751 1890 |
| Inv:Rev | Accsee docs | missing | 1 1 1 1 0 0 1 -2 -3 -3 1 -5 -6 -8 -8 1 -9 -4 -4 -10 -10 1 -14 11 26 30 6 6 1 -20 50 85 134 162 42 |
| Inv:Rev | AccRevsee docs | missing | 1 0 1 0 -1 0 0 -1 -4 -3 0 -2 -3 -9 -8 0 -6 -6 -1 -11 -10 0 -24 -20 -5 20 5 6 0 -120 -92 -43 -8 62 |
| Inv:Rev | AntiDiagsee docs | missing | 1 1 1 0 1 -1 1 -3 0 1 -6 -1 1 -10 -1 0 1 -15 5 -2 1 -21 25 0 0 1 -28 70 15 -6 1 -36 154 35 4 0 1 |
| Inv:Rev | Diffx1T(n, k) (k+1) | missing | 1 1 0 1 -2 0 1 -6 -3 0 1 -12 -3 -8 0 1 -20 15 0 -30 0 1 -30 75 60 20 -144 0 1 -42 210 140 245 168 |
| Inv:Rev | RowSum∑ k=0..n T(n, k) | A176118 | 1 1 0 -3 -8 -10 6 42 -160 -2952 -27720 -253440 -2553528 -28562664 -349272000 -4618376280 |
| Inv:Rev | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 1 1 0 0 0 30 0 392 -4032 9720 -336600 871992 -38084904 112875672 -6059289600 19782929280 |
| Inv:Rev | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 0 -1 -3 -8 -10 -24 42 -552 1080 -37440 83160 -3425520 9522240 -462147672 1440913320 -85398001920 |
| Inv:Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A005727 | 1 1 2 3 8 10 54 -42 944 -5112 47160 -419760 4297512 -47607144 575023344 -7500202920 105180931200 |
| Inv:Rev | AbsSum∑ k=0..n | T(n, k) | | missing | 1 1 2 5 10 22 84 324 1336 8166 61454 520940 4999422 53618008 630968324 8068178720 111396089176 |
| Inv:Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 1 0 -2 -6 -10 -11 5 52 158 275 281 -445 -2581 -7919 -13197 -13592 39286 167332 581798 739797 |
| Inv:Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 2 1 -7 -26 -36 66 496 1016 -3312 -49680 -436272 -4145448 -45972096 -570098424 -7658244120 |
| Inv:Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 1 -1 -8 -22 -34 -18 -118 -2616 -29160 -282960 -2858448 -31603944 -382467864 -5018253576 |
| Inv:Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 1 3 6 30 600 5880 18239760 435037680 68769684547200 84388489622236800 723633960319757625600 |
| Inv:Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | A114890 | 1 1 1 3 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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 | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 1 3 6 10 25 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 |
| Inv:Rev | ColMiddleT(n, n // 2) | missing | 1 1 -1 -3 -1 5 15 35 49 -231 -1365 -3003 -7645 35321 311311 667095 2475473 -11321167 -132652377 |
| Inv:Rev | CentralET(2 n, n) | A298511 | 1 -1 -1 15 49 -1365 -7645 311311 2475473 -132652377 -1367593305 90881245455 1151541572401 |
| Inv:Rev | CentralOT(2 n + 1, n) | missing | 1 -3 5 35 -231 -3003 35321 667095 -11321167 -280043907 6216178605 190024422315 -5212705798535 |
| 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 -1 -11 -37 -29 502 4012 17999 43171 -93629 -1736965 -10217612 -15805568 470437528 9107848986 |
| Inv:Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -1 3 -7 27 -71 370 -680 8015 12341 372031 2830563 38292628 460951568 6421791272 93716919894 |
| Inv:Rev | TransNat0∑ k=0..n T(n, k) k | missing | 0 0 -1 -5 -14 -24 -24 -160 -2456 -26208 -255240 -2605008 -29050416 -353905200 -4668981576 |
| Inv:Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 1 -1 -8 -22 -34 -18 -118 -2616 -29160 -282960 -2858448 -31603944 -382467864 -5018253576 |
| Inv:Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 0 -1 -7 -28 -86 -316 -2262 -22240 -226368 -2386128 -26952960 -330105744 -4372022448 -62252363304 |
| Inv:Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 2 2 -6 -40 -100 72 1848 8192 8352 -139680 -1235520 -6657792 -37195392 -382335744 -5807571840 |
| Inv:Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A265945 | 1 -2 6 -18 64 -220 888 -3192 15104 -48096 338400 -285120 13728768 75484032 1327431168 15621137280 |
| Inv:Rev | DiagRow1T(n + 1, n) | A000142 | 1 -1 -1 -2 -6 -24 -120 -720 -5040 -40320 -362880 -3628800 -39916800 -479001600 -6227020800 |
| Inv:Rev | DiagRow2T(n + 2, n) | A045406 | 1 -3 -1 0 4 28 188 1368 11016 98208 964512 10370880 121337280 1535880960 20924455680 305396421120 |
| Inv:Rev | DiagRow3T(n + 3, n) | A347276 | 1 -6 5 15 49 196 944 5340 34716 254760 2078856 18620784 180973584 1887504768 20887922304 |
| Inv:Rev | DiagCol1T(n + 1, 1) | A000217 | 0 -1 -3 -6 -10 -15 -21 -28 -36 -45 -55 -66 -78 -91 -105 -120 -136 -153 -171 -190 -210 -231 -253 |
| Inv:Rev | DiagCol2T(n + 2, 2) | A059302 | 0 -1 -1 5 25 70 154 294 510 825 1265 1859 2639 3640 4900 6460 8364 10659 13395 16625 20405 24794 |
| Inv:Rev | DiagCol3T(n + 3, 3) | missing | 0 -2 0 15 35 0 -252 -1050 -2970 -6930 -14300 -27027 -47775 -80080 -128520 -198900 -298452 -436050 |
| Inv:Rev | Polysee docs | missing | 1 1 1 1 1 1 1 0 1 1 1 -3 -1 1 1 1 -8 -9 -2 1 1 1 -10 -31 -17 -3 1 1 1 6 -95 -80 -27 -4 1 1 1 42 |
| 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 | 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 | PolyRow3∑ k=0..3 T(3, k) n^k | A014209 | 1 -3 -9 -17 -27 -39 -53 -69 -87 -107 -129 -153 -179 -207 -237 -269 -303 -339 -377 -417 -459 -503 |
| Inv:Rev | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 1 -1 -9 -31 -95 -513 -5481 -72511 -1059327 -17258625 -314205705 -6342349407 -140644383711 |
| Inv:Rev | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 1 -2 -17 -80 -470 -4922 -75194 -1384688 -29410424 -710697320 -19293134960 -581540653592 |
| Inv:Rev | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 1 -1 -17 -167 -3674 -177389 -13514346 -1454033503 -209912367752 -39165967369449 -9173351458491120 |
| << | 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.