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E.g.f. satisfies A(x) = exp( x * (1+x)^2 * A(x) ).
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%I #11 May 03 2023 09:11:07

%S 1,1,7,58,725,11816,239047,5794972,163861609,5299694704,193052158091,

%T 7823764856084,349236133422013,17028109232138824,900544754206010383,

%U 51348494205747851116,3140366001277974883793,205067625446428300157408

%N E.g.f. satisfies A(x) = exp( x * (1+x)^2 * A(x) ).

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.

%F E.g.f.: exp( -LambertW(-x * (1+x)^2) ).

%F a(n) = n! * Sum_{k=0..n} (k+1)^(k-1) * binomial(2*k,n-k)/k!.

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-x*(1+x)^2))))

%Y Cf. A000272, A362771.

%K nonn

%O 0,3

%A _Seiichi Manyama_, May 02 2023