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 A382674 #17 Apr 06 2025 03:48:28
%S A382674 1,1,1,1,5,1,1,13,13,1,1,29,77,29,1,1,61,325,325,61,1,1,125,1181,2357,
%T A382674 1181,125,1,1,253,3973,13621,13621,3973,253,1,1,509,12797,69269,
%U A382674 118061,69269,12797,509,1,1,1021,40165,326005,862261,862261,326005,40165,1021,1
%N A382674 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where A(n,k) = n! * k! * [x^n * y^k] exp(x+y) / (exp(x) + exp(y) - exp(x+y))^4.
%F A382674 E.g.f.: exp(x+y) / (exp(x) + exp(y) - exp(x+y))^4.
%F A382674 A(n,k) = A(k,n).
%F A382674 A(n,k) = Sum_{j=0..min(n,k)} (j!)^2 * binomial(j+3,3) * Stirling2(n+1,j+1) * Stirling2(k+1,j+1).
%e A382674 Square array begins:
%e A382674 1, 1, 1, 1, 1, 1, ...
%e A382674 1, 5, 13, 29, 61, 125, ...
%e A382674 1, 13, 77, 325, 1181, 3973, ...
%e A382674 1, 29, 325, 2357, 13621, 69269, ...
%e A382674 1, 61, 1181, 13621, 118061, 862261, ...
%e A382674 1, 125, 3973, 69269, 862261, 8712245, ...
%e A382674 ...
%o A382674 (PARI) a(n, k) = sum(j=0, min(n, k), j!^2*binomial(j+3, 3)*stirling(n+1, j+1, 2)*stirling(k+1, j+1, 2));
%Y A382674 Columns k=0..2 give A000012, A036563(n+2), A382677.
%Y A382674 Main diagonal gives A382678.
%Y A382674 Cf. A099594, A136126, A382673.
%Y A382674 Cf. A382736.
%K A382674 nonn,tabl
%O A382674 0,5
%A A382674 _Seiichi Manyama_, Apr 03 2025