A362303 a(n) = n! * Sum_{k=0..floor(n/3)} (-n/6)^k * binomial(n-2*k,k)/(n-2*k)!.

1, 1, 1, -2, -15, -49, 241, 3186, 17473, -136835, -2591199, -19940194, 214217521, 5280969123, 52303886545, -714177220574, -21687847310079, -262685369226919, 4351534043729473, 157014580915662750, 2248361900084617201, -43790588385118719689

Offset: 0

Author

Seiichi Manyama, Apr 15 2023

Keywords

• sign

Links

• Winston de Greef, Table of n, a(n) for n = 0..441
• Eric Weisstein's World of Mathematics, Lambert W-Function.

Crossrefs

Main diagonal of A362302.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((2*lambertw(x^3/2))^(1/3))/(1+lambertw(x^3/2))))

Formula

a(n) = n! * [x^n] exp(x - n*x^3/6).

E.g.f.: exp( ( 2*LambertW(x^3/2) )^(1/3) ) / (1 + LambertW(x^3/2)).