A362348 a(n) = n! * Sum_{k=0..floor(n/3)} k^k / (k! * (n-3*k)!).

1, 1, 1, 7, 25, 61, 1561, 10291, 40657, 1754425, 16632721, 90479071, 5469933481, 67591594357, 468224398825, 36386954606731, 554182030325281, 4663003095358321, 442756825853252257, 8014853488848923575, 79354642490200806841, 8901962495566386752941

Offset: 0

Author

Seiichi Manyama, Apr 17 2023

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..427
• Eric Weisstein's World of Mathematics, Lambert W-Function.

Crossrefs

Cf. A086331, A362347, A362349.

Programs

PARI

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

Formula

E.g.f.: exp(x) / (1 + LambertW(-x^3)).

a(n) ~ (exp(3*exp(-1/3)/2) + 2*cos(sqrt(3)*exp(-1/3)/2 - 2*Pi*n/3)) * n^n / (sqrt(3) * exp(2*n/3 + exp(-1/3)/2)). - Vaclav Kotesovec, Apr 18 2023