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 A376492 #12 Feb 16 2025 08:34:07
%S A376492 1,0,2,6,60,600,7680,123480,2212560,47053440,1104092640,29200802400,
%T A376492 845985349440,26864561243520,924556913280000,34334318184566400,
%U A376492 1367790957223891200,58194757879908249600,2633788044958380710400,126340003102675832870400
%N A376492 E.g.f. satisfies A(x) = exp(x^2 * (1 + x) * A(x)^2).
%H A376492 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A376492 E.g.f.: exp( -LambertW(-2*x^2 * (1+x))/2 ).
%F A376492 a(n) = n! * Sum_{k=0..floor(n/2)} (2*k+1)^(k-1) * binomial(k,n-2*k)/k!.
%o A376492 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-2*x^2*(1+x))/2)))
%o A376492 (PARI) a(n) = n!*sum(k=0, n\2, (2*k+1)^(k-1)*binomial(k, n-2*k)/k!);
%Y A376492 Cf. A362771, A376493.
%Y A376492 Cf. A376476.
%K A376492 nonn
%O A376492 0,3
%A A376492 _Seiichi Manyama_, Sep 25 2024