A362321 a(n) = n! * Sum_{k=0..floor(n/4)} n^k /(k! * (n-4*k)!).

1, 1, 1, 1, 97, 601, 2161, 5881, 1303681, 14723857, 90770401, 402581521, 139389608161, 2284512533161, 19946635524817, 122623661651401, 57728368477678081, 1240234284406887841, 14010634784751445441, 110117252571345122977

Offset: 0

Author

Seiichi Manyama, Apr 16 2023

Keywords

• nonn

Links

• Winston de Greef, Table of n, a(n) for n = 0..408
• Eric Weisstein's World of Mathematics, Lambert W-Function.

Crossrefs

Cf. A362301, A362323.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(exp((-lambertw(-4*x^4)/4)^(1/4))/(1+lambertw(-4*x^4))))

Formula

a(n) = n! * [x^n] exp(x + n*x^4).

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