%I #19 May 01 2023 09:25:14
%S 1,0,0,6,24,60,840,10290,80976,847224,13306320,190271070,2677088040,
%T 46082426676,874515884424,16582066303530,336875275380000,
%U 7539189088358640,176554878235711776,4295134487197296054,111114287924643309240,3036073975138066955820
%N Expansion of e.g.f. 1/(1 - x^3 * exp(x)).
%H Seiichi Manyama, <a href="/A358081/b358081.txt">Table of n, a(n) for n = 0..431</a>
%F a(n) = n! * Sum_{k=0..floor(n/3)} k^(n - 3*k)/(n - 3*k)!.
%F a(n) ~ n! / ((1 + LambertW(1/3)) * 3^(n+1) * LambertW(1/3)^n). - _Vaclav Kotesovec_, Oct 30 2022
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x^3*exp(x))))
%o (PARI) a(n) = n!*sum(k=0, n\3, k^(n-3*k)/(n-3*k)!);
%Y Cf. A006153, A358080.
%Y Cf. A292889, A355575, A358065.
%K nonn,easy
%O 0,4
%A _Seiichi Manyama_, Oct 30 2022