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 A253670 #5 Jan 19 2015 06:51:16 %S A253670 1,1,1,1,3,1,1,5,5,1,1,7,21,7,1,1,9,43,49,9,1,1,11,73,229,89,11,1,1, %T A253670 13,111,529,685,141,13,1,1,15,157,1021,3393,1531,205,15,1,1,17,211, %U A253670 1753,8501,12361,2887,281,17,1,1,19,273,2773,18001,63591,32809,4873,369,19,1 %N A253670 Square array read by ascending antidiagonals, T(n, k) = k!*[x^k](exp(x)*sum(j=0..n, C(2*n,j)*x^j)), n>=0, k>=0. %F A253670 T(n,n) = A082545(n). %e A253670 Square array starts: %e A253670 [n\k][0 1 2 3 4 5 6] %e A253670 [0] 1, 1, 1, 1, 1, 1, 1, ... %e A253670 [1] 1, 3, 5, 7, 9, 11, 13, ... %e A253670 [2] 1, 5, 21, 49, 89, 141, 205, ... %e A253670 [3] 1, 7, 43, 229, 685, 1531, 2887, ... %e A253670 [4] 1, 9, 73, 529, 3393, 12361, 32809, ... %e A253670 [5] 1, 11, 111, 1021, 8501, 63591, 272851, ... %e A253670 [6] 1, 13, 157, 1753, 18001, 169021, 1442173, ... %e A253670 The first few rows as a triangle: %e A253670 1 %e A253670 1, 1 %e A253670 1, 3, 1 %e A253670 1, 5, 5, 1 %e A253670 1, 7, 21, 7, 1 %e A253670 1, 9, 43, 49, 9, 1 %e A253670 1, 11, 73, 229, 89, 11, 1 %p A253670 T := (n,k) -> k!*coeff(series(exp(x)*add(binomial(2*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 A253670 Cf. A082545. %K A253670 nonn,tabl %O A253670 0,5 %A A253670 _Peter Luschny_, Jan 18 2015