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 A365054 #19 Feb 16 2025 08:34:06
%S A365054 1,1,6,64,1038,22666,624448,20801628,813473468,36543076444,
%T A365054 1854702411336,104970490358944,6555275229438664,447773277245296536,
%U A365054 33211911279540910400,2658266282912883209296,228375288313274403201552,20961681963345040127314192
%N A365054 E.g.f. satisfies A(x) = exp( x * (1+x/2) * A(x)^2 ).
%H A365054 Seiichi Manyama, <a href="/A365054/b365054.txt">Table of n, a(n) for n = 0..348</a>
%H A365054 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A365054 E.g.f.: exp( -LambertW(-2*x * (1+x/2))/2 ).
%F A365054 a(n) = n! * Sum_{k=0..n} (1/2)^(n-k) * (2*k+1)^(k-1) * binomial(k,n-k)/k!.
%F A365054 From _Vaclav Kotesovec_, Nov 10 2023: (Start)
%F A365054 E.g.f.: sqrt(-LambertW(-2*x * (1+x/2)) / (2*x * (1+x/2))).
%F A365054 a(n) ~ sqrt((-sqrt(1 + exp(-1)) + 1 + exp(-1))/2) * n^(n-1) / (exp(n-1) * (-1 + sqrt(1 + exp(-1)))^n). (End)
%o A365054 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-2*x*(1+x/2))/2)))
%Y A365054 Cf. A365053, A365055, A365056.
%Y A365054 Cf. A362474, A362773.
%K A365054 nonn
%O A365054 0,3
%A A365054 _Seiichi Manyama_, Aug 19 2023