A358065 - OEIS

%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