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
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula and Mats Granvik, Mar 10 2013
STATUS
approved