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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.

%I A225678 #5 May 13 2013 01:42:11
%S A225678 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 A225678 0,0,1,114,606,-1168,-96,816,-272,0,1,240,2832,-2176,-8832,11904,
%U A225678 -3968,0,0,1,494,11122,11072,-83360,71168,13312,-31744,7936,0,1,1004
%N 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.
%e A225678 [0]                1
%e A225678 [1]              0, 1
%e A225678 [2]             0, 1, 0
%e A225678 [3]           0, 1, 2, -2
%e A225678 [4]          0, 1, 8, -8, 0
%e A225678 [5]      0, 1, 22, -6, -32, 16
%e A225678 [6]    0, 1, 52, 84, -272, 136, 0
%p A225678 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 A225678 Cf. A141720.
%K A225678 sign,tabl
%O A225678 0,9
%A A225678 _Peter Luschny_, May 12 2013