A362320 a(n) = n! * Sum_{k=0..floor(n/5)} (-n/5)^k / (k! * (n-5*k)!).

1, 1, 1, 1, 1, -119, -863, -3527, -10751, -27215, 7197121, 96476689, 689534209, 3507486841, 14238448225, -5835497948279, -114117547235327, -1164586980639263, -8296447373407871, -46351121024513375, 25734702161134932481, 661538303263860440041

Offset: 0

Author

Seiichi Manyama, Apr 16 2023

Keywords

• sign

Links

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

Crossrefs

Cf. A362276, A362304, A362315.

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)).