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, 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

Offset: 0

Author

Peter Luschny, May 12 2013

Keywords

• sign
• tabl

Examples

			[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
		

Crossrefs

Cf. A141720.

Programs

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);