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%I #5 May 13 2013 01:42:11
%S 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,
%T 0,0,1,114,606,-1168,-96,816,-272,0,1,240,2832,-2176,-8832,11904,
%U -3968,0,0,1,494,11122,11072,-83360,71168,13312,-31744,7936,0,1,1004
%N 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.
%e [0] 1
%e [1] 0, 1
%e [2] 0, 1, 0
%e [3] 0, 1, 2, -2
%e [4] 0, 1, 8, -8, 0
%e [5] 0, 1, 22, -6, -32, 16
%e [6] 0, 1, 52, 84, -272, 136, 0
%p 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);
%Y Cf. A141720.
%K sign,tabl
%O 0,9
%A _Peter Luschny_, May 12 2013
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