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A225678 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. 1
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,9

LINKS

Table of n, a(n) for n=0..57.

EXAMPLE

[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

MAPLE

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);

CROSSREFS

Cf. A141720.

Sequence in context: A029583 A011289 A288387 * A141720 A248017 A244606

Adjacent sequences:  A225675 A225676 A225677 * A225679 A225680 A225681

KEYWORD

sign,tabl

AUTHOR

Peter Luschny, May 12 2013

STATUS

approved

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Last modified June 20 11:38 EDT 2019. Contains 324234 sequences. (Running on oeis4.)