Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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