A358065 Expansion of e.g.f. 1/(1 - x * exp(x^3)).

1, 1, 2, 6, 48, 360, 2880, 27720, 322560, 4173120, 58665600, 911433600, 15567552000, 287740252800, 5710178073600, 121450256928000, 2758495490150400, 66563938106265600, 1699990278213427200, 45828946821385728000, 1300703752243703808000

Offset: 0

Author

Seiichi Manyama, Oct 29 2022

Keywords

• nonn
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..425

Crossrefs

Cf. A354553, A358064.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x*exp(x^3))))

PARI

a(n) = n!*sum(k=0, n\3, (n-3*k)^k/k!);

Formula

a(n) = n! * Sum_{k=0..floor(n/3)} (n - 3*k)^k/k!.

a(n) ~ n! * 3^(n/3) / ((1 + LambertW(3)) * LambertW(3)^(n/3)). - Vaclav Kotesovec, Nov 01 2022