A362319 a(n) = n! * Sum_{k=0..floor(n/5)} (n/5)^k / (k! * (n-5*k)!).

1, 1, 1, 1, 1, 121, 865, 3529, 10753, 27217, 7318081, 96720625, 689990401, 3508289929, 14239793569, 5933573525881, 114415115802625, 1165402803391009, 8298505279241857, 46355961619888993, 26167218073714552321, 663290722580370585625

Offset: 0

Author

Seiichi Manyama, Apr 16 2023

Keywords

• nonn

Links

• Winston de Greef, Table of n, a(n) for n = 0..434
• Eric Weisstein's World of Mathematics, Lambert W-Function.

Crossrefs

Cf. A277614, A362300, A362314.

Programs

PARI

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

Formula

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

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