A362305 a(n) = n! * Sum_{k=0..floor(n/3)} (-n)^k * binomial(n-2*k,k)/(n-2*k)!.

1, 1, 1, -17, -95, -299, 12241, 122011, 642433, -41645015, -597247199, -4407324569, 390913189921, 7315513279933, 69439658097265, -7816418805235949, -180448412456686079, -2093964182367814319, 285679499679525805633, 7844019340520912230495

Offset: 0

Author

Seiichi Manyama, Apr 15 2023

Keywords

• sign

Links

• Winston de Greef, Table of n, a(n) for n = 0..402
• Eric Weisstein's World of Mathematics, Lambert W-Function.

Crossrefs

Cf. A362301, A362302.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(exp((lambertw(3*x^3)/3)^(1/3))/(1+lambertw(3*x^3))))

Formula

a(n) = A362302(n,6*n).

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

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