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 A362772 #12 Feb 16 2025 08:34:05
%S A362772 1,1,7,58,725,11816,239047,5794972,163861609,5299694704,193052158091,
%T A362772 7823764856084,349236133422013,17028109232138824,900544754206010383,
%U A362772 51348494205747851116,3140366001277974883793,205067625446428300157408
%N A362772 E.g.f. satisfies A(x) = exp( x * (1+x)^2 * A(x) ).
%H A362772 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A362772 E.g.f.: exp( -LambertW(-x * (1+x)^2) ).
%F A362772 a(n) = n! * Sum_{k=0..n} (k+1)^(k-1) * binomial(2*k,n-k)/k!.
%o A362772 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-x*(1+x)^2))))
%Y A362772 Cf. A000272, A362771.
%K A362772 nonn
%O A362772 0,3
%A A362772 _Seiichi Manyama_, May 02 2023