A362324 a(n) = n! * Sum_{k=0..floor(n/5)} (-n)^k / (k! * (n-5*k)!).

1, 1, 1, 1, 1, -599, -4319, -17639, -53759, -136079, 181137601, 2414356561, 17242917121, 87695201881, 355974659041, -734340892685399, -14279571631503359, -145614163414530719, -1037158816523518079, -5794132157196668639, 16192314610730781350401

Offset: 0

Author

Seiichi Manyama, Apr 16 2023

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..414
• Eric Weisstein's World of Mathematics, Lambert W-Function.

Crossrefs

Cf. A362282, A362305, A362322.

Cf. A351906, A362320.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((lambertw(5*x^5)/5)^(1/5))/(1+lambertw(5*x^5))))

Formula

a(n) = n! * [x^n] exp(x - n*x^5).

E.g.f.: exp( ( LambertW(5*x^5)/5 )^(1/5) ) / (1 + LambertW(5*x^5)).