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 A382804 #14 Apr 05 2025 16:09:35
%S A382804 1,2,14,260,9588,581952,52096512,6423520896,1041005447424,
%T A382804 214260350714496,54547409318781312,16820040059243046144,
%U A382804 6175245603727007034624,2661063379044058584861696,1329787781176741647226481664,762665713456216694195942866944
%N A382804 a(n) = Sum_{k=0..n} k! * (k+1)! * Stirling1(n,k)^2.
%F A382804 a(n) == 0 (mod 2) for n > 0.
%F A382804 a(n) = (n!)^2 * [(x*y)^n] 1 / (1 - log(1-x) * log(1-y))^2.
%F A382804 a(n) = (n!)^2 * [(x*y)^n] 1 / (1 - log(1+x) * log(1+y))^2.
%F A382804 a(n) ~ sqrt(Pi) * n^(2*n + 3/2) / (exp(1) - 1)^(2*n+2). - _Vaclav Kotesovec_, Apr 05 2025
%o A382804 (PARI) a(n) = sum(k=0, n, k!*(k+1)!*stirling(n, k, 1)^2);
%Y A382804 Main diagonal of A382799.
%Y A382804 Cf. A382792, A382806.
%Y A382804 Cf. A382737.
%K A382804 nonn
%O A382804 0,2
%A A382804 _Seiichi Manyama_, Apr 05 2025