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 A253667 #5 Jan 18 2015 21:11:59 %S A253667 1,1,-1,1,0,1,1,1,-1,-1,1,2,-1,2,1,1,3,1,-1,-3,-1,1,4,5,-4,5,4,1,1,5, %T A253667 11,-1,1,-11,-5,-1,1,6,19,14,-15,14,19,6,1,1,7,29,47,-19,19,-47,-29, %U A253667 -7,-1,1,8,41,104,37,-56,37,104,41,8,1 %N A253667 Square array read by ascending antidiagonals, T(n, k) = k!*[x^k](exp(-x) *sum(j=0..n, C(n,j)*x^j)), n>=0, k>=0. %F A253667 T(n,n) = A009940(n). %e A253667 Square array starts: %e A253667 [n\k][0 1 2 3 4 5 6] %e A253667 [0] 1, -1, 1, -1, 1, -1, 1, ... %e A253667 [1] 1, 0, -1, 2, -3, 4, -5, ... %e A253667 [2] 1, 1, -1, -1, 5, -11, 19, ... %e A253667 [3] 1, 2, 1, -4, 1, 14, -47, ... %e A253667 [4] 1, 3, 5, -1, -15, 19, 37, ... %e A253667 [5] 1, 4, 11, 14, -19, -56, 151, ... %e A253667 [6] 1, 5, 19, 47, 37, -151, -185, ... %e A253667 The first few rows as a triangle: %e A253667 1, %e A253667 1, -1, %e A253667 1, 0, 1, %e A253667 1, 1, -1, -1, %e A253667 1, 2, -1, 2, 1, %e A253667 1, 3, 1, -1, -3, -1, %e A253667 1, 4, 5, -4, 5, 4, 1. %p A253667 T := (n,k) -> k!*coeff(series(exp(-x)*add(binomial(n,j)*x^j, j=0..n), x, k+1), x, k): for n from 0 to 6 do lprint(seq(T(n,k),k=0..6)) od; %Y A253667 Cf. A009940. %K A253667 sign,tabl %O A253667 0,12 %A A253667 _Peter Luschny_, Jan 18 2015