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

0,5

Links

Winston de Greef, Table of n, a(n) for n = 0..408

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

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)).

Prog

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

Crossrefs

Cf. A362301, A362323.

Sequence in context: A142765 A144130 A144131 * A130833 A130873 A193411

Adjacent sequences: A362318 A362319 A362320 * A362322 A362323 A362324

Keyword

nonn

Author

Seiichi Manyama, Apr 16 2023

Status

approved