A362345 a(n) = n! * Sum_{k=0..floor(n/4)} (-n/24)^k /(k! * (n-4*k)!).

1, 1, 1, 1, -3, -24, -89, -244, 1681, 24382, 155401, 695146, -7490339, -157336464, -1421454033, -8817579224, 129268310081, 3555528110716, 41578411339441, 329824291072252, -6116622750516899, -207991913454970784, -2985298421745508329

Offset: 0

Author

Seiichi Manyama, Apr 16 2023

Keywords

• sign

Links

• Eric Weisstein's World of Mathematics, Lambert W-Function.

Crossrefs

Cf. A362303, A362346.

Cf. A351930.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((6*lambertw(x^4/6))^(1/4))/(1+lambertw(x^4/6))))

Formula

a(n) = n! * [x^n] exp(x - n*x^4/24).

E.g.f.: exp( ( 6*LambertW(x^4/6) )^(1/4) ) / (1 + LambertW(x^4/6)).