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 A362892 #14 May 19 2025 03:07:19
%S A362892 1,0,0,6,12,20,1470,10122,47096,1814472,25119450,226527950,6732015972,
%T A362892 142901684796,2071229736758,57596022404130,1589579741044080,
%U A362892 32832196825559312,951335638952843826,31043287459520549910,838738470701197009820
%N A362892 Expansion of e.g.f. 1/(1 + LambertW(-x^2 * (exp(x) - 1))).
%H A362892 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A362892 a(n) = n! * Sum_{k=0..floor(n/3)} k^k * Stirling2(n-2*k,k)/(n-2*k)!.
%F A362892 a(n) ~ n^n / (sqrt((2+r)*exp(r) - 2) * r^(n+1) * exp(n + 1/2)), where r = 0.640353588740603511543638690178204955926349... is the root of the equation r^2*(exp(r+1) - exp(1)) = 1. - _Vaclav Kotesovec_, May 19 2025
%t A362892 With[{nn=20},CoefficientList[Series[1/(1+LambertW[-x^2(Exp[x]-1)]),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, May 14 2025 *)
%o A362892 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1+lambertw(-x^2*(exp(x)-1)))))
%Y A362892 Cf. A282190, A362836.
%Y A362892 Cf. A240989, A362891.
%K A362892 nonn
%O A362892 0,4
%A A362892 _Seiichi Manyama_, May 08 2023