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 A382806 #9 Apr 05 2025 16:09:31
%S A382806 1,3,27,588,24612,1669128,165049224,22269896064,3918921022656,
%T A382806 870149951146944,237662482188210624,78249086559726140160,
%U A382806 30547324837444471084800,13946361918619108837939200,7359961832428044552536217600,4444946383758589481684168540160
%N A382806 a(n) = Sum_{k=0..n} (k!)^2 * binomial(k+2,2) * Stirling1(n,k)^2.
%F A382806 a(n) == 0 (mod 3) for n > 0.
%F A382806 a(n) = (n!)^2 * [(x*y)^n] 1 / (1 - log(1-x) * log(1-y))^3.
%F A382806 a(n) = (n!)^2 * [(x*y)^n] 1 / (1 - log(1+x) * log(1+y))^3.
%F A382806 a(n) ~ sqrt(Pi) * n^(2*n + 5/2) / (2 * (exp(1) - 1)^(2*n+3)). - _Vaclav Kotesovec_, Apr 05 2025
%o A382806 (PARI) a(n) = sum(k=0, n, k!^2*binomial(k+2, 2)*stirling(n, k, 1)^2);
%Y A382806 Main diagonal of A382800.
%Y A382806 Cf. A382792, A382804.
%Y A382806 Cf. A382738.
%K A382806 nonn
%O A382806 0,2
%A A382806 _Seiichi Manyama_, Apr 05 2025