OEIS Similars: A008279, A068424, A094587, A173333, A181511
| ↕ Type | ↕ Trait | ↕ Anum | ↕ Sequence |
|---|---|---|---|
| Std | TriangleT(n, k), 0 ≤ k ≤ n | A008279 | 1 1 1 1 2 2 1 3 6 6 1 4 12 24 24 1 5 20 60 120 120 1 6 30 120 360 720 720 1 7 42 210 840 2520 5040 |
| Std | RevT(n, n - k), 0 ≤ k ≤ n | A094587 | 1 1 1 2 2 1 6 6 3 1 24 24 12 4 1 120 120 60 20 5 1 720 720 360 120 30 6 1 5040 5040 2520 840 210 42 |
| Std | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A128229 | 1 -1 1 0 -2 1 0 0 -3 1 0 0 0 -4 1 0 0 0 0 -5 1 0 0 0 0 0 -6 1 0 0 0 0 0 0 -7 1 0 0 0 0 0 0 0 -8 1 0 |
| Std | Accsee docs | A347667 | 1 1 2 1 3 5 1 4 10 16 1 5 17 41 65 1 6 26 86 206 326 1 7 37 157 517 1237 1957 1 8 50 260 1100 3620 |
| Std | AccRevsee docs | A367962 | 1 1 2 2 4 5 6 12 15 16 24 48 60 64 65 120 240 300 320 325 326 720 1440 1800 1920 1950 1956 1957 |
| Std | AntiDiagsee docs | A344391 | 1 1 1 1 1 2 1 3 2 1 4 6 1 5 12 6 1 6 20 24 1 7 30 60 24 1 8 42 120 120 1 9 56 210 360 120 1 10 72 |
| Std | Diffx1T(n, k) (k+1) | A121757 | 1 1 2 1 4 6 1 6 18 24 1 8 36 96 120 1 10 60 240 600 720 1 12 90 480 1800 4320 5040 1 14 126 840 |
| Std | RowSum∑ k=0..n T(n, k) | A000522 | 1 2 5 16 65 326 1957 13700 109601 986410 9864101 108505112 1302061345 16926797486 236975164805 |
| Std | EvenSum∑ k=0..n T(n, k) even(k) | A087208 | 1 1 3 7 37 141 1111 5923 62217 426457 5599531 46910271 739138093 7318002277 134523132927 |
| Std | OddSum∑ k=0..n T(n, k) odd(k) | A002747 | 0 1 2 9 28 185 846 7777 47384 559953 4264570 61594841 562923252 9608795209 102452031878 |
| Std | AltSum∑ k=0..n T(n, k) (-1)^k | A000166 | 1 0 1 -2 9 -44 265 -1854 14833 -133496 1334961 -14684570 176214841 -2290792932 32071101049 |
| Std | AbsSum∑ k=0..n | T(n, k) | | A000522 | 1 2 5 16 65 326 1957 13700 109601 986410 9864101 108505112 1302061345 16926797486 236975164805 |
| Std | DiagSum∑ k=0..n // 2 T(n - k, k) | A072374 | 1 1 2 3 6 11 24 51 122 291 756 1979 5526 15627 46496 140451 442194 1414931 4687212 15785451 |
| Std | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A111063 | 1 3 9 31 129 651 3913 27399 219201 1972819 19728201 217010223 2604122689 33853594971 473950329609 |
| Std | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A001339 | 1 3 11 49 261 1631 11743 95901 876809 8877691 98641011 1193556233 15624736141 220048367319 |
| Std | RowLcmLcm k=0..n | T(n, k) | > 1 | A000142 | 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 |
| Std | RowGcdGcd k=0..n | T(n, k) | > 1 | A000027 | 1 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 | RowMaxMax k=0..n | T(n, k) | | A000142 | 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 |
| Std | ColMiddleT(n, n // 2) | A205825 | 1 1 2 3 12 20 120 210 1680 3024 30240 55440 665280 1235520 17297280 32432400 518918400 980179200 |
| Std | CentralET(2 n, n) | A001813 | 1 2 12 120 1680 30240 665280 17297280 518918400 17643225600 670442572800 28158588057600 |
| Std | CentralOT(2 n + 1, n) | A006963 | 1 3 20 210 3024 55440 1235520 32432400 980179200 33522128640 1279935820800 53970627110400 |
| 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) | A000142 | 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 |
| Std | BinConv∑ k=0..n C(n, k) T(n, k) | A002720 | 1 2 7 34 209 1546 13327 130922 1441729 17572114 234662231 3405357682 53334454417 896324308634 |
| Std | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A009940 | 1 0 -1 -4 -15 -56 -185 -204 6209 112400 1520271 19165420 237686449 2944654296 36392001815 |
| Std | TransNat0∑ k=0..n T(n, k) k | A093964 | 0 1 6 33 196 1305 9786 82201 767208 7891281 88776910 1085051121 14322674796 203121569833 |
| Std | TransNat1∑ k=0..n T(n, k) (k + 1) | A001339 | 1 3 11 49 261 1631 11743 95901 876809 8877691 98641011 1193556233 15624736141 220048367319 |
| Std | TransSqrs∑ k=0..n T(n, k) k^2 | A343276 | 0 1 10 81 652 5545 50886 506905 5480056 64116657 808856290 10959016321 158851484100 2454385635481 |
| Std | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A010842 | 1 3 10 38 168 872 5296 37200 297856 2681216 26813184 294947072 3539368960 46011804672 644165281792 |
| Std | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A000023 | 1 -1 2 -2 8 8 112 656 5504 49024 491264 5401856 64826368 842734592 11798300672 176974477312 |
| Std | DiagRow1T(n + 1, n) | A000142 | 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 1307674368000 |
| Std | DiagRow2T(n + 2, n) | A001710 | 1 3 12 60 360 2520 20160 181440 1814400 19958400 239500800 3113510400 43589145600 653837184000 |
| Std | DiagRow3T(n + 3, n) | A001715 | 1 4 20 120 840 6720 60480 604800 6652800 79833600 1037836800 14529715200 217945728000 3487131648000 |
| Std | DiagCol1T(n + 1, 1) | A000027 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 |
| Std | DiagCol2T(n + 2, 2) | A002378 | 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 | DiagCol3T(n + 3, 3) | A007531 | 6 24 60 120 210 336 504 720 990 1320 1716 2184 2730 3360 4080 4896 5814 6840 7980 9240 10626 12144 |
| Std | Polysee docs | missing | 1 1 1 1 2 1 1 5 3 1 1 16 13 4 1 1 65 79 25 5 1 1 326 633 226 41 6 1 1 1957 6331 2713 493 61 7 1 1 |
| Std | PolyRow1∑ k=0..1 T(1, k) n^k | A000027 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 |
| Std | PolyRow2∑ k=0..2 T(2, k) n^k | A001844 | 1 5 13 25 41 61 85 113 145 181 221 265 313 365 421 481 545 613 685 761 841 925 1013 1105 1201 1301 |
| Std | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 1 16 79 226 493 916 1531 2374 3481 4888 6631 8746 11269 14236 17683 21646 26161 31264 36991 43378 |
| Std | PolyCol2∑ k=0..n T(n, k) 2^k | A010844 | 1 3 13 79 633 6331 75973 1063623 17017969 306323443 6126468861 134782314943 3234775558633 |
| Std | PolyCol3∑ k=0..n T(n, k) 3^k | A010845 | 1 4 25 226 2713 40696 732529 15383110 369194641 9968255308 299047659241 9868572754954 |
| Std | PolyDiag∑ k=0..n T(n, k) n^k | A277452 | 1 2 13 226 7889 458026 39684637 4788052298 766526598721 157108817646514 40104442275129101 |
| Alt | TriangleT(n, k), 0 ≤ k ≤ n | A008279 | 1 1 -1 1 -2 2 1 -3 6 -6 1 -4 12 -24 24 1 -5 20 -60 120 -120 1 -6 30 -120 360 -720 720 1 -7 42 -210 |
| Alt | RevT(n, n - k), 0 ≤ k ≤ n | A094587 | 1 -1 1 2 -2 1 -6 6 -3 1 24 -24 12 -4 1 -120 120 -60 20 -5 1 720 -720 360 -120 30 -6 1 -5040 5040 |
| Alt | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A128229 | 1 1 1 0 2 1 0 0 3 1 0 0 0 4 1 0 0 0 0 5 1 0 0 0 0 0 6 1 0 0 0 0 0 0 7 1 0 0 0 0 0 0 0 8 1 0 0 0 0 0 |
| Alt | Accsee docs | missing | 1 1 0 1 -1 1 1 -2 4 -2 1 -3 9 -15 9 1 -4 16 -44 76 -44 1 -5 25 -95 265 -455 265 1 -6 36 -174 666 |
| Alt | AccRevsee docs | missing | 1 -1 0 2 0 1 -6 0 -3 -2 24 0 12 8 9 -120 0 -60 -40 -45 -44 720 0 360 240 270 264 265 -5040 0 -2520 |
| Alt | AntiDiagsee docs | A344391 | 1 1 1 -1 1 -2 1 -3 2 1 -4 6 1 -5 12 -6 1 -6 20 -24 1 -7 30 -60 24 1 -8 42 -120 120 1 -9 56 -210 360 |
| Alt | Diffx1T(n, k) (k+1) | A121757 | 1 1 -2 1 -4 6 1 -6 18 -24 1 -8 36 -96 120 1 -10 60 -240 600 -720 1 -12 90 -480 1800 -4320 5040 1 |
| Alt | RowSum∑ k=0..n T(n, k) | A000166 | 1 0 1 -2 9 -44 265 -1854 14833 -133496 1334961 -14684570 176214841 -2290792932 32071101049 |
| Alt | EvenSum∑ k=0..n T(n, k) even(k) | A087208 | 1 1 3 7 37 141 1111 5923 62217 426457 5599531 46910271 739138093 7318002277 134523132927 |
| Alt | OddSum∑ k=0..n T(n, k) odd(k) | A002747 | 0 -1 -2 -9 -28 -185 -846 -7777 -47384 -559953 -4264570 -61594841 -562923252 -9608795209 |
| Alt | AltSum∑ k=0..n T(n, k) (-1)^k | A000522 | 1 2 5 16 65 326 1957 13700 109601 986410 9864101 108505112 1302061345 16926797486 236975164805 |
| Alt | AbsSum∑ k=0..n | T(n, k) | | A000522 | 1 2 5 16 65 326 1957 13700 109601 986410 9864101 108505112 1302061345 16926797486 236975164805 |
| Alt | DiagSum∑ k=0..n // 2 T(n - k, k) | A358603 | 1 1 0 -1 0 3 2 -9 -12 35 78 -153 -544 723 4170 -3337 -35028 10851 320678 57255 -3178152 -2190253 |
| Alt | AccSum∑ k=0..n ∑ j=0..k T(n, j) | 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 | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A000255 | 1 -1 3 -11 53 -309 2119 -16687 148329 -1468457 16019531 -190899411 2467007773 -34361893981 |
| Alt | RowLcmLcm k=0..n | T(n, k) | > 1 | A000142 | 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 |
| Alt | RowGcdGcd k=0..n | T(n, k) | > 1 | A000027 | 1 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 |
| Alt | RowMaxMax k=0..n | T(n, k) | | A000142 | 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 |
| Alt | ColMiddleT(n, n // 2) | A205825 | 1 1 -2 -3 12 20 -120 -210 1680 3024 -30240 -55440 665280 1235520 -17297280 -32432400 518918400 |
| Alt | CentralET(2 n, n) | A001813 | 1 -2 12 -120 1680 -30240 665280 -17297280 518918400 -17643225600 670442572800 -28158588057600 |
| Alt | CentralOT(2 n + 1, n) | A006963 | 1 -3 20 -210 3024 -55440 1235520 -32432400 980179200 -33522128640 1279935820800 -53970627110400 |
| 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) | A000142 | 1 -1 2 -6 24 -120 720 -5040 40320 -362880 3628800 -39916800 479001600 -6227020800 87178291200 |
| Alt | BinConv∑ k=0..n C(n, k) T(n, k) | A009940 | 1 0 -1 4 -15 56 -185 204 6209 -112400 1520271 -19165420 237686449 -2944654296 36392001815 |
| Alt | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A002720 | 1 -2 7 -34 209 -1546 13327 -130922 1441729 -17572114 234662231 -3405357682 53334454417 |
| Alt | TransNat0∑ k=0..n T(n, k) k | A000166 | 0 -1 2 -9 44 -265 1854 -14833 133496 -1334961 14684570 -176214841 2290792932 -32071101049 |
| Alt | TransNat1∑ k=0..n T(n, k) (k + 1) | A000255 | 1 -1 3 -11 53 -309 2119 -16687 148329 -1468457 16019531 -190899411 2467007773 -34361893981 |
| Alt | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 -1 6 -33 212 -1545 12714 -116809 1186632 -13216113 160195310 -2099893521 29604093276 |
| Alt | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A000023 | 1 1 2 2 8 -8 112 -656 5504 -49024 491264 -5401856 64826368 -842734592 11798300672 -176974477312 |
| Alt | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A010842 | 1 -3 10 -38 168 -872 5296 -37200 297856 -2681216 26813184 -294947072 3539368960 -46011804672 |
| Alt | DiagRow1T(n + 1, n) | A000142 | 1 -2 6 -24 120 -720 5040 -40320 362880 -3628800 39916800 -479001600 6227020800 -87178291200 |
| Alt | DiagRow2T(n + 2, n) | A001710 | 1 -3 12 -60 360 -2520 20160 -181440 1814400 -19958400 239500800 -3113510400 43589145600 |
| Alt | DiagRow3T(n + 3, n) | A001715 | 1 -4 20 -120 840 -6720 60480 -604800 6652800 -79833600 1037836800 -14529715200 217945728000 |
| Alt | DiagCol1T(n + 1, 1) | A000027 | -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 -13 -14 -15 -16 -17 -18 -19 -20 -21 -22 -23 -24 -25 -26 -27 |
| Alt | DiagCol2T(n + 2, 2) | A002378 | 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 |
| Alt | DiagCol3T(n + 3, 3) | A007531 | -6 -24 -60 -120 -210 -336 -504 -720 -990 -1320 -1716 -2184 -2730 -3360 -4080 -4896 -5814 -6840 |
| Alt | Polysee docs | missing | 1 1 1 1 0 1 1 1 -1 1 1 -2 5 -2 1 1 9 -29 13 -3 1 1 -44 233 -116 25 -4 1 1 265 -2329 1393 -299 41 -5 |
| Alt | PolyRow1∑ k=0..1 T(1, k) n^k | A000027 | 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 -13 -14 -15 -16 -17 -18 -19 -20 -21 -22 -23 -24 -25 -26 |
| Alt | PolyRow2∑ k=0..2 T(2, k) n^k | A001844 | 1 1 5 13 25 41 61 85 113 145 181 221 265 313 365 421 481 545 613 685 761 841 925 1013 1105 1201 |
| Alt | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 1 -2 -29 -116 -299 -614 -1097 -1784 -2711 -3914 -5429 -7292 -9539 -12206 -15329 -18944 -23087 |
| Alt | PolyCol2∑ k=0..n T(n, k) 2^k | A000354 | 1 -1 5 -29 233 -2329 27949 -391285 6260561 -112690097 2253801941 -49583642701 1190007424825 |
| Alt | PolyCol3∑ k=0..n T(n, k) 3^k | A000180 | 1 -2 13 -116 1393 -20894 376093 -7897952 189550849 -5117872922 153536187661 -5066694192812 |
| Alt | PolyDiag∑ k=0..n T(n, k) n^k | A319392 | 1 0 5 -116 4785 -307024 28435285 -3598112580 596971515329 -125802906617600 32834740225688901 |
| Rev | TriangleT(n, k), 0 ≤ k ≤ n | A094587 | 1 1 1 2 2 1 6 6 3 1 24 24 12 4 1 120 120 60 20 5 1 720 720 360 120 30 6 1 5040 5040 2520 840 210 42 |
| Rev | InvT-1(n, k), 0 ≤ k ≤ n | A128229 | 1 -1 1 0 -2 1 0 0 -3 1 0 0 0 -4 1 0 0 0 0 -5 1 0 0 0 0 0 -6 1 0 0 0 0 0 0 -7 1 0 0 0 0 0 0 0 -8 1 0 |
| Rev | RevInvT-1(n, n - k), 0 ≤ k ≤ n | A127701 | 1 1 -1 1 -2 0 1 -3 0 0 1 -4 0 0 0 1 -5 0 0 0 0 1 -6 0 0 0 0 0 1 -7 0 0 0 0 0 0 1 -8 0 0 0 0 0 0 0 1 |
| Rev | Accsee docs | A367962 | 1 1 2 2 4 5 6 12 15 16 24 48 60 64 65 120 240 300 320 325 326 720 1440 1800 1920 1950 1956 1957 |
| Rev | AccRevsee docs | A347667 | 1 1 2 1 3 5 1 4 10 16 1 5 17 41 65 1 6 26 86 206 326 1 7 37 157 517 1237 1957 1 8 50 260 1100 3620 |
| Rev | AntiDiagsee docs | missing | 1 1 2 1 6 2 24 6 1 120 24 3 720 120 12 1 5040 720 60 4 40320 5040 360 20 1 362880 40320 2520 120 5 |
| Rev | Diffx1T(n, k) (k+1) | missing | 1 1 2 2 4 3 6 12 9 4 24 48 36 16 5 120 240 180 80 25 6 720 1440 1080 480 150 36 7 5040 10080 7560 |
| Rev | RowSum∑ k=0..n T(n, k) | A000522 | 1 2 5 16 65 326 1957 13700 109601 986410 9864101 108505112 1302061345 16926797486 236975164805 |
| Rev | EvenSum∑ k=0..n T(n, k) even(k) | A009179 | 1 1 3 9 37 185 1111 7777 62217 559953 5599531 61594841 739138093 9608795209 134523132927 |
| Rev | OddSum∑ k=0..n T(n, k) odd(k) | A186763 | 0 1 2 7 28 141 846 5923 47384 426457 4264570 46910271 562923252 7318002277 102452031878 |
| Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A000166 | 1 0 1 2 9 44 265 1854 14833 133496 1334961 14684570 176214841 2290792932 32071101049 481066515734 |
| Rev | AbsSum∑ k=0..n | T(n, k) | | A000522 | 1 2 5 16 65 326 1957 13700 109601 986410 9864101 108505112 1302061345 16926797486 236975164805 |
| Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | A003470 | 1 1 3 8 31 147 853 5824 45741 405845 4012711 43733976 520795003 6726601063 93651619881 |
| Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A001339 | 1 3 11 49 261 1631 11743 95901 876809 8877691 98641011 1193556233 15624736141 220048367319 |
| Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A111063 | 1 3 9 31 129 651 3913 27399 219201 1972819 19728201 217010223 2604122689 33853594971 473950329609 |
| Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | A000142 | 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 |
| Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | A000027 | 1 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 | RowMaxMax k=0..n | T(n, k) | | A000142 | 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 |
| Rev | ColMiddleT(n, n // 2) | A081125 | 1 1 2 6 12 60 120 840 1680 15120 30240 332640 665280 8648640 17297280 259459200 518918400 |
| Rev | CentralET(2 n, n) | A001813 | 1 2 12 120 1680 30240 665280 17297280 518918400 17643225600 670442572800 28158588057600 |
| Rev | CentralOT(2 n + 1, n) | A000407 | 1 6 60 840 15120 332640 8648640 259459200 8821612800 335221286400 14079294028800 647647525324800 |
| Rev | ColLeftT(n, 0) | A000142 | 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 |
| 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) | A002720 | 1 2 7 34 209 1546 13327 130922 1441729 17572114 234662231 3405357682 53334454417 896324308634 |
| Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A009940 | 1 0 -1 4 -15 56 -185 204 6209 -112400 1520271 -19165420 237686449 -2944654296 36392001815 |
| Rev | TransNat0∑ k=0..n T(n, k) k | A007526 | 0 1 4 15 64 325 1956 13699 109600 986409 9864100 108505111 1302061344 16926797485 236975164804 |
| Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | A111063 | 1 3 9 31 129 651 3913 27399 219201 1972819 19728201 217010223 2604122689 33853594971 473950329609 |
| Rev | TransSqrs∑ k=0..n T(n, k) k^2 | A030297 | 0 1 6 27 124 645 3906 27391 219192 1972809 19728190 217010211 2604122676 33853594957 473950329594 |
| Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A010844 | 1 3 13 79 633 6331 75973 1063623 17017969 306323443 6126468861 134782314943 3234775558633 |
| Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A000354 | 1 -1 5 -29 233 -2329 27949 -391285 6260561 -112690097 2253801941 -49583642701 1190007424825 |
| Rev | DiagRow1T(n + 1, n) | A000027 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 |
| Rev | DiagRow2T(n + 2, n) | A002378 | 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 |
| Rev | DiagRow3T(n + 3, n) | A007531 | 6 24 60 120 210 336 504 720 990 1320 1716 2184 2730 3360 4080 4896 5814 6840 7980 9240 10626 12144 |
| Rev | DiagCol1T(n + 1, 1) | A000142 | 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 1307674368000 |
| Rev | DiagCol2T(n + 2, 2) | A001710 | 1 3 12 60 360 2520 20160 181440 1814400 19958400 239500800 3113510400 43589145600 653837184000 |
| Rev | DiagCol3T(n + 3, 3) | A001715 | 1 4 20 120 840 6720 60480 604800 6652800 79833600 1037836800 14529715200 217945728000 3487131648000 |
| Rev | Polysee docs | A134558 | 1 1 1 2 2 1 6 5 3 1 24 16 10 4 1 120 65 38 17 5 1 720 326 168 78 26 6 1 5040 1957 872 393 142 37 7 |
| Rev | PolyRow1∑ k=0..1 T(1, k) n^k | A000027 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 |
| Rev | PolyRow2∑ k=0..2 T(2, k) n^k | A002522 | 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 | missing | 6 16 38 78 142 236 366 538 758 1032 1366 1766 2238 2788 3422 4146 4966 5888 6918 8062 9326 10716 |
| Rev | PolyCol2∑ k=0..n T(n, k) 2^k | A010842 | 1 3 10 38 168 872 5296 37200 297856 2681216 26813184 294947072 3539368960 46011804672 644165281792 |
| Rev | PolyCol3∑ k=0..n T(n, k) 3^k | A053486 | 1 4 17 78 393 2208 13977 100026 806769 7280604 72865089 801693126 9620848953 125072630712 |
| Rev | PolyDiag∑ k=0..n T(n, k) n^k | A063170 | 1 2 10 78 824 10970 176112 3309110 71219584 1727242866 46602156800 1384438376222 44902138752000 |
| Rev:Inv | TriangleT(n, k), 0 ≤ k ≤ n | A128229 | 1 -1 1 0 -2 1 0 0 -3 1 0 0 0 -4 1 0 0 0 0 -5 1 0 0 0 0 0 -6 1 0 0 0 0 0 0 -7 1 0 0 0 0 0 0 0 -8 1 0 |
| Rev:Inv | RevT(n, n - k), 0 ≤ k ≤ n | A127701 | 1 1 -1 1 -2 0 1 -3 0 0 1 -4 0 0 0 1 -5 0 0 0 0 1 -6 0 0 0 0 0 1 -7 0 0 0 0 0 0 1 -8 0 0 0 0 0 0 0 1 |
| Rev:Inv | InvT-1(n, k), 0 ≤ k ≤ n | A094587 | 1 1 1 2 2 1 6 6 3 1 24 24 12 4 1 120 120 60 20 5 1 720 720 360 120 30 6 1 5040 5040 2520 840 210 42 |
| Rev:Inv | RevInvT-1(n, n - k), 0 ≤ k ≤ n | A008279 | 1 1 1 1 2 2 1 3 6 6 1 4 12 24 24 1 5 20 60 120 120 1 6 30 120 360 720 720 1 7 42 210 840 2520 5040 |
| Rev:Inv | Accsee docs | missing | 1 -1 0 0 -2 -1 0 0 -3 -2 0 0 0 -4 -3 0 0 0 0 -5 -4 0 0 0 0 0 -6 -5 0 0 0 0 0 0 -7 -6 0 0 0 0 0 0 0 |
| Rev:Inv | AccRevsee docs | missing | 1 1 0 1 -1 -1 1 -2 -2 -2 1 -3 -3 -3 -3 1 -4 -4 -4 -4 -4 1 -5 -5 -5 -5 -5 -5 1 -6 -6 -6 -6 -6 -6 -6 |
| Rev:Inv | AntiDiagsee docs | missing | 1 -1 0 1 0 -2 0 0 1 0 0 -3 0 0 0 1 0 0 0 -4 0 0 0 0 1 0 0 0 0 -5 0 0 0 0 0 1 0 0 0 0 0 -6 0 0 0 0 0 |
| Rev:Inv | Diffx1T(n, k) (k+1) | missing | 1 -1 2 0 -4 3 0 0 -9 4 0 0 0 -16 5 0 0 0 0 -25 6 0 0 0 0 0 -36 7 0 0 0 0 0 0 -49 8 0 0 0 0 0 0 0 |
| Rev:Inv | RowSum∑ k=0..n T(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 |
| Rev:Inv | EvenSum∑ k=0..n T(n, k) even(k) | A093178 | 1 -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 |
| Rev:Inv | OddSum∑ k=0..n T(n, k) odd(k) | A124625 | 0 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 |
| Rev:Inv | AltSum∑ k=0..n T(n, k) (-1)^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 |
| Rev:Inv | AbsSum∑ k=0..n | T(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:Inv | DiagSum∑ k=0..n // 2 T(n - k, k) | A057979 | 1 -1 1 -2 1 -3 1 -4 1 -5 1 -6 1 -7 1 -8 1 -9 1 -10 1 -11 1 -12 1 -13 1 -14 1 -15 1 -16 1 -17 1 -18 |
| Rev:Inv | AccSum∑ k=0..n ∑ j=0..k T(n, j) | 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 |
| Rev:Inv | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A028387 | 1 1 -1 -5 -11 -19 -29 -41 -55 -71 -89 -109 -131 -155 -181 -209 -239 -271 -305 -341 -379 -419 -461 |
| Rev:Inv | RowLcmLcm k=0..n | T(n, k) | > 1 | A000027 | 1 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 | RowGcdGcd k=0..n | T(n, k) | > 1 | A000027 | 1 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 | RowMaxMax k=0..n | T(n, k) | | A000027 | 1 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 | ColMiddleT(n, n // 2) | A130779 | 1 -1 -2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| Rev:Inv | CentralET(2 n, n) | A130706 | 1 -2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| Rev:Inv | CentralOT(2 n + 1, 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 |
| 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) | A005563 | 1 0 -3 -8 -15 -24 -35 -48 -63 -80 -99 -120 -143 -168 -195 -224 -255 -288 -323 -360 -399 -440 -483 |
| Rev:Inv | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^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:Inv | TransNat0∑ k=0..n T(n, k) 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 |
| Rev:Inv | TransNat1∑ k=0..n T(n, k) (k + 1) | A028387 | 1 1 -1 -5 -11 -19 -29 -41 -55 -71 -89 -109 -131 -155 -181 -209 -239 -271 -305 -341 -379 -419 -461 |
| Rev:Inv | TransSqrs∑ k=0..n T(n, k) k^2 | A318765 | 0 1 2 -3 -20 -55 -114 -203 -328 -495 -710 -979 -1308 -1703 -2170 -2715 -3344 -4063 -4878 -5795 |
| Rev:Inv | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^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 |
| Rev:Inv | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^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:Inv | DiagRow1T(n + 1, n) | A000027 | -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 -13 -14 -15 -16 -17 -18 -19 -20 -21 -22 -23 -24 -25 -26 -27 |
| Rev:Inv | DiagCol1T(n + 1, 1) | A130706 | 1 -2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| Rev:Inv | DiagCol2T(n + 2, 2) | A169585 | 1 -3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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:Inv | DiagCol3T(n + 3, 3) | A261595 | 1 -4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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:Inv | Polysee docs | missing | 1 -1 1 0 0 1 0 -1 1 1 0 -2 0 2 1 0 -3 -4 3 3 1 0 -4 -16 0 8 4 1 0 -5 -48 -27 16 15 5 1 0 -6 -128 |
| Rev:Inv | PolyRow1∑ k=0..1 T(1, k) n^k | A000027 | -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 |
| Rev: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 |
| Rev:Inv | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 0 -2 -4 0 16 50 108 196 320 486 700 968 1296 1690 2156 2700 3328 4046 4860 5776 6800 7938 9196 |
| Rev:Inv | PolyCol2∑ k=0..n T(n, k) 2^k | A058922 | 1 1 0 -4 -16 -48 -128 -320 -768 -1792 -4096 -9216 -20480 -45056 -98304 -212992 -458752 -983040 |
| Rev:Inv | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 2 3 0 -27 -162 -729 -2916 -10935 -39366 -137781 -472392 -1594323 -5314410 -17537553 -57395628 |
| Rev:Inv | PolyDiag∑ k=0..n T(n, k) n^k | A000007 | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| << | 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.