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 A224228 Matrix inverse of the triangle of Eulerian numbers T(n,k), 0<=k<=n, read by rows. 0
 1, 1, 1, 5, 4, 1, 65, 55, 11, 1, 1993, 1668, 352, 26, 1, 131665, 110421, 23084, 1784, 57, 1, 18010589, 15099584, 3161545, 242630, 8031, 120, 1, 4981731137, 4176740483, 874335823, 67166609, 2212739, 33933, 247, 1, 2752004906353, 2307299944904, 483009645152, 37100594596, 1222926298, 18699092, 138602, 502, 1, 3017738824824961, 2530094418968969, 529648104311800, 40683406518208, 1340952746858, 20509601522, 151765114, 556366, 1013, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS This sequence arose from discussion of a binomial inverse matrix made by Mats Granik and posted to Active Mathematica Yahoo group. Row sums are:1, 2, 10, 132, 4040, 267012, 36522500, 10102220972, 5580656855500, 6119526369294812, ... LINKS Eric W. Weisstein's World of Mathematics, Eulerian Number FORMULA Matrix inverse of Eulerian triangle as a matrix: Inverse(A123125) MATHEMATICA As posted in discussion on Active Mathematica yahoo group: It gives a Sierpinski triangle...<< Combinatorica` << Notation` Table[If[k <= n, Eulerian[n + 1, k], 0], {n, 0, 5}, {k, 0, 5}] f[n_, k_] = If[k <= n, Eulerian[n + 1, k], 0] Clear[x, n, k, A, B, nn] A[m_] := Table[ Table[f[n - 1, k - 1]*If[n > k, (-1)^Floor[(n - k + 1)/2], 1], {k, 1, m}], {n, 1, m}] B[m_] := Inverse[A[m]] Table[TableForm[B[m]], {m, 1, 10}] Table[Apply[Plus, B[10][[m]]], {m, 1, Length[B[10]]}] a = Table[Table[B[10][[m, n]], {n, 1, m}], {m, 1, Length[B[10]]}] Flatten[a] ListDensityPlot[Mod[B[128], 4]] MatrixPlot[Mod[B[128], 4]] CROSSREFS Cf. A008292, A123125. Sequence in context: A108440 A102220 A279151 * A286680 A201680 A349409 Adjacent sequences: A224225 A224226 A224227 * A224229 A224230 A224231 KEYWORD nonn,tabl AUTHOR Roger L. Bagula and Mats Granvik, Mar 10 2013 STATUS approved

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Last modified March 22 17:42 EDT 2023. Contains 361432 sequences. (Running on oeis4.)