A362322 a(n) = n! * Sum_{k=0..floor(n/4)} (-n)^k / (k! * (n-4*k)!).

1, 1, 1, 1, -95, -599, -2159, -5879, 1276801, 14669425, 90669601, 402407281, -136515598559, -2275742812199, -19922903656655, -122565283331399, 56538094207096321, 1235380139032068961, 13993348375743336001, 110062069784059565665

Offset: 0

Author

Seiichi Manyama, Apr 16 2023

Keywords

• sign

Links

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

Crossrefs

Cf. A362282, A362305, A362324.

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)).