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 A376493 #12 Feb 16 2025 08:34:07
%S A376493 1,0,0,6,24,0,2520,35280,141120,6048000,181440000,1995840000,
%T A376493 51831964800,2280127449600,47882676441600,1192991325926400,
%U A376493 59048471978496000,1942527607308288000,56983429057076121600,2842216483159788134400,126830901998902413312000
%N A376493 E.g.f. satisfies A(x) = exp(x^3 * (1 + x) * A(x)^3).
%H A376493 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A376493 E.g.f.: exp( -LambertW(-3*x^3 * (1+x))/3 ).
%F A376493 a(n) = n! * Sum_{k=0..floor(n/3)} (3*k+1)^(k-1) * binomial(k,n-3*k)/k!.
%o A376493 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-3*x^3*(1+x))/3)))
%o A376493 (PARI) a(n) = n!*sum(k=0, n\3, (3*k+1)^(k-1)*binomial(k, n-3*k)/k!);
%Y A376493 Cf. A362771, A376492.
%Y A376493 Cf. A376477.
%K A376493 nonn
%O A376493 0,4
%A A376493 _Seiichi Manyama_, Sep 25 2024