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 A382678 #10 Apr 04 2025 06:21:37
%S A382678 1,5,77,2357,118061,8712245,886143917,118592620277,20176999414061,
%T A382678 4249819031692085,1084956766012858157,329975948760472311797,
%U A382678 117851658189070970988461,48830366210401091606537525,23228207308210113849419226797,12571433948267218576823401692917
%N A382678 a(n) = Sum_{k=0..n} (k!)^2 * binomial(k+3,3) * Stirling2(n+1,k+1)^2.
%F A382678 a(n) = (n!)^2 * [(x*y)^n] exp(x+y) / (exp(x) + exp(y) - exp(x+y))^4.
%o A382678 (PARI) a(n) = sum(k=0, n, k!^2*binomial(k+3, 3)*stirling(n+1, k+1, 2)^2);
%Y A382678 Main diagonal of A382674.
%Y A382678 Cf. A048163, A092552, A382676.
%K A382678 nonn
%O A382678 0,2
%A A382678 _Seiichi Manyama_, Apr 03 2025