A362349 a(n) = n! * Sum_{k=0..floor(n/4)} k^k / (k! * (n-4*k)!).

1, 1, 1, 1, 25, 121, 361, 841, 82321, 728785, 3633841, 13313521, 2195435881, 28125394441, 196393341145, 981274727161, 227100486456481, 3807339471993121, 34186011461595361, 216366574074187105, 64438384450412161081, 1335035336388170601241

Offset: 0

Author

Seiichi Manyama, Apr 17 2023

Keywords

• nonn

Links

• Winston de Greef, Table of n, a(n) for n = 0..431
• Eric Weisstein's World of Mathematics, Lambert W-Function.

Crossrefs

Cf. A086331, A362347, A362348.

Programs

PARI

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

Formula

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