A362304 a(n) = n! * Sum_{k=0..floor(n/3)} (-n/3)^k * binomial(n-2*k,k)/(n-2*k)!.

1, 1, 1, -5, -31, -99, 1201, 13231, 70785, -1362311, -21562399, -161746749, 4263108961, 87979472725, 849097038609, -28416142768649, -723086288422399, -8532476619366159, 346207723221680065, 10474480743776327179, 146105160034616914401

Offset: 0

Author

Seiichi Manyama, Apr 15 2023

Keywords

• sign

Links

• Winston de Greef, Table of n, a(n) for n = 0..425
• Eric Weisstein's World of Mathematics, Lambert W-Function.

Crossrefs

Cf. A362300, A362302.

Programs

PARI

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

Formula

a(n) = A362302(n,2*n).

a(n) = n! * [x^n] exp(x - n*x^3/3).

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