This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A373572 #6 Jun 16 2024 04:47:06 %S A373572 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 A373572 1,1,8,-38,18,117,-212,117,18,-38,8,1,-1,-19,52,143,-677,818,0,-818, %U A373572 677,-143,-52,19,1,1,38,-6,-817,2196,-722,-5071,8762,-5071,-722,2196,-817,-6,38,1 %N A373572 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 A373572 Triangle starts: %e A373572 [0] [1] %e A373572 [1] [-1, 1] %e A373572 [2] [ 1, -2, 1] %e A373572 [3] [-1, 2, 0, -2, 1] %e A373572 [4] [ 1, -1, -5, 10, -5, -1, 1] %e A373572 [5] [-1, -2, 18, -26, 0, 26, -18, 2, 1] %e A373572 [6] [ 1, 8, -38, 18, 117, -212, 117, 18, -38, 8, 1] %e A373572 [7] [-1, -19, 52, 143, -677, 818, 0, -818, 677, -143, -52, 19, 1] %p A373572 EZP((n, k) -> (-1)^(n-k)*binomial(n, k), 8); # Using function EZP from A373432. %Y A373572 Cf. A373432, A205497, A373657, A000007 (row sums). %K A373572 sign,tabf %O A373572 0,5 %A A373572 _Peter Luschny_, Jun 15 2024