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 A362836 #14 May 19 2025 05:06:36
%S A362836 1,0,2,3,52,245,4086,36547,663832,8984313,184262770,3334315391,
%T A362836 77900601780,1751855308645,46508427942718,1241853335819475,
%U A362836 37195023972070576,1144511291020453361,38337497638919397738,1331709923436162817447
%N A362836 Expansion of e.g.f. 1/(1 + LambertW(-x * (exp(x) - 1))).
%F A362836 a(n) = n! * Sum_{k=0..floor(n/2)} k^k * Stirling2(n-k,k)/(n-k)!.
%F A362836 a(n) ~ n^n / (sqrt(exp(r)*(1+r) - 1) * r^(n + 1/2) * exp(n + 1/2)), where r = 0.528399250336668412340528181936966763473... is the root of the equation exp(1+r)-exp(1) = 1/r. - _Vaclav Kotesovec_, May 19 2025
%o A362836 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1+lambertw(-x*(exp(x)-1)))))
%Y A362836 Cf. A290158, A362835.
%K A362836 nonn
%O A362836 0,3
%A A362836 _Seiichi Manyama_, May 05 2023