A362346 a(n) = n! * Sum_{k=0..floor(n/5)} (-n/120)^k /(k! * (n-5*k)!).

1, 1, 1, 1, 1, -4, -35, -146, -447, -1133, 10081, 162625, 1188001, 6073354, 24692669, -340585244, -8007557375, -83565282891, -598436312543, -3348919070207, 62583951520321, 1933207863670000, 26224985071994941, 241528060568764586, 1721188205642283841

Offset: 0

Author

Seiichi Manyama, Apr 16 2023

Keywords

• sign

Links

• Winston de Greef, Table of n, a(n) for n = 0..483
• Eric Weisstein's World of Mathematics, Lambert W-Function.

Crossrefs

Cf. A362303, A362345.

Cf. A351931.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((24*lambertw(x^5/24))^(1/5))/(1+lambertw(x^5/24))))

Formula

a(n) = n! * [x^n] exp(x - n*x^5/120).

E.g.f.: exp( ( 24*LambertW(x^5/24) )^(1/5) ) / (1 + LambertW(x^5/24)).