%I #17 Nov 01 2022 12:16:34
%S 1,1,2,6,48,360,2880,27720,322560,4173120,58665600,911433600,
%T 15567552000,287740252800,5710178073600,121450256928000,
%U 2758495490150400,66563938106265600,1699990278213427200,45828946821385728000,1300703752243703808000
%N Expansion of e.g.f. 1/(1 - x * exp(x^3)).
%H Seiichi Manyama, <a href="/A358065/b358065.txt">Table of n, a(n) for n = 0..425</a>
%F a(n) = n! * Sum_{k=0..floor(n/3)} (n - 3*k)^k/k!.
%F a(n) ~ n! * 3^(n/3) / ((1 + LambertW(3)) * LambertW(3)^(n/3)). - _Vaclav Kotesovec_, Nov 01 2022
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x*exp(x^3))))
%o (PARI) a(n) = n!*sum(k=0, n\3, (n-3*k)^k/k!);
%Y Cf. A354553, A358064.
%K nonn,easy
%O 0,3
%A _Seiichi Manyama_, Oct 29 2022
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