A362323 a(n) = n! * Sum_{k=0..floor(n/5)} n^k / (k! * (n-5*k)!).

1, 1, 1, 1, 1, 601, 4321, 17641, 53761, 136081, 181742401, 2415576241, 17245198081, 87699217321, 355981385761, 736792782125401, 14287010845685761, 145634558983324321, 1037210264169367681, 5794253172081059041, 16246379099801447769601

Offset: 0

Author

Seiichi Manyama, Apr 16 2023

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..414
• Eric Weisstein's World of Mathematics, Lambert W-Function.

Crossrefs

Cf. A362301, A362321.

Cf. A190877, A362319.

Programs

PARI

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

Formula

a(n) = n! * [x^n] exp(x + n*x^5).

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