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A225678
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Triangle read by rows, T(n,k) = sum_{j=0..n} (-1)^(n+k+j) A(n,j)*C(j,n-k), A(n,j) the Eulerian numbers; n >= 0, k >= 0.
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1
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1, 0, 1, 0, 1, 0, 0, 1, 2, -2, 0, 1, 8, -8, 0, 0, 1, 22, -6, -32, 16, 0, 1, 52, 84, -272, 136, 0, 0, 1, 114, 606, -1168, -96, 816, -272, 0, 1, 240, 2832, -2176, -8832, 11904, -3968, 0, 0, 1, 494, 11122, 11072, -83360, 71168, 13312, -31744, 7936, 0, 1, 1004
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graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,9
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LINKS
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EXAMPLE
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[0] 1
[1] 0, 1
[2] 0, 1, 0
[3] 0, 1, 2, -2
[4] 0, 1, 8, -8, 0
[5] 0, 1, 22, -6, -32, 16
[6] 0, 1, 52, 84, -272, 136, 0
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MAPLE
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with(combinat): A225678 := (n, k) -> add((-1)^(n+k+j)*eulerian1(n, j) *binomial(j, n-k), j=0..n); seq(print(seq(A225678(n, k), k=0..n)), n=0..8);
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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