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 A376100 #14 Feb 16 2025 08:34:07
%S A376100 0,1,6,57,760,13265,289116,7600873,234730224,8340307137,335388171700,
%T A376100 15062758093361,747393408423432,40606032733746961,2397539426985311532,
%U A376100 152864047998089113785,10467226142002168282336,766094017043351707135745
%N A376100 Expansion of e.g.f. -LambertW(-x / (1 - 2*x)).
%H A376100 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A376100 E.g.f. A(x) satisfies A(x) = x * (2*A(x) + exp(A(x))).
%F A376100 E.g.f.: Series_Reversion( x / (2*x + exp(x)) ).
%F A376100 a(n) = n! * Sum_{k=1..n} 2^(n-k) * k^(k-1) * binomial(n-1,k-1)/k!.
%F A376100 a(n) ~ (1 + 2*exp(-1))^(n + 1/2) * n^(n-1). - _Vaclav Kotesovec_, Sep 10 2024
%o A376100 (PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-lambertw(-x/(1-2*x)))))
%o A376100 (PARI) a(n) = n!*sum(k=1, n, 2^(n-k)*k^(k-1)*binomial(n-1, k-1)/k!);
%Y A376100 Cf. A052871, A376101.
%K A376100 nonn
%O A376100 0,3
%A A376100 _Seiichi Manyama_, Sep 10 2024