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%I #6 Jun 16 2024 04:47:06
%S 1,-1,1,1,-2,1,-1,2,0,-2,1,1,-1,-5,10,-5,-1,1,-1,-2,18,-26,0,26,-18,2,
%T 1,1,8,-38,18,117,-212,117,18,-38,8,1,-1,-19,52,143,-677,818,0,-818,
%U 677,-143,-52,19,1,1,38,-6,-817,2196,-722,-5071,8762,-5071,-722,2196,-817,-6,38,1
%N Triangle read by rows: Coefficients of the polynomials P(n, x) * EZ(n, x), where P denote the signed Pascal polynomials and EZ the Eulerian zig-zag polynomials A205497.
%e Triangle starts:
%e [0] [1]
%e [1] [-1, 1]
%e [2] [ 1, -2, 1]
%e [3] [-1, 2, 0, -2, 1]
%e [4] [ 1, -1, -5, 10, -5, -1, 1]
%e [5] [-1, -2, 18, -26, 0, 26, -18, 2, 1]
%e [6] [ 1, 8, -38, 18, 117, -212, 117, 18, -38, 8, 1]
%e [7] [-1, -19, 52, 143, -677, 818, 0, -818, 677, -143, -52, 19, 1]
%p EZP((n, k) -> (-1)^(n-k)*binomial(n, k), 8); # Using function EZP from A373432.
%Y Cf. A373432, A205497, A373657, A000007 (row sums).
%K sign,tabf
%O 0,5
%A _Peter Luschny_, Jun 15 2024
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