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 A384492 #10 May 31 2025 09:34:32
%S A384492 1,2,113,38992,47071264,147015606528,988250901343488,
%T A384492 12631667044878213120,280790763724247161061376,
%U A384492 10147405862241529912885248000,565550513462476798468573003776000,46592777163703224212146175606784000000,5479872142880875751798643810680954683392000
%N A384492 a(n) = n!^3 * Sum_{k=0..n} Stirling2(2*k,k) * Stirling2(2*n-2*k,n-k) / binomial(n,k)^3.
%F A384492 a(n) ~ Pi * 2^(2*n+2) * n^(4*n+1) / (sqrt(1-w) * exp(4*n) * (2-w)^n * w^n), where w = -LambertW(-2*exp(-2)) = -A226775 = 0.4063757399599599...
%t A384492 Table[n!^3 * Sum[StirlingS2[2*k, k] * StirlingS2[2*n-2*k, n-k] / Binomial[n, k]^3, {k, 0, n}], {n, 0, 15}]
%o A384492 (PARI) a(n) = n!^3 * sum(k=0, n, stirling(2*k,k,2) * stirling(2*n-2*k,n-k,2) / binomial(n,k)^3); \\ _Michel Marcus_, May 31 2025
%Y A384492 Cf. A187655, A384470, A384491.
%Y A384492 Cf. A187657, A384471, A384472.
%K A384492 nonn
%O A384492 0,2
%A A384492 _Vaclav Kotesovec_, May 31 2025