A362315 a(n) = n! * Sum_{k=0..floor(n/4)} (-n/4)^k /(k! * (n-4*k)!).

1, 1, 1, 1, -23, -149, -539, -1469, 77281, 911737, 5657401, 25134121, -2065730039, -35352993389, -310739232803, -1913714425349, 213881558916481, 4797269708789041, 54560246286936241, 429606655679843857, -60718212515535701399, -1684610587476711352709

Offset: 0

Author

Seiichi Manyama, Apr 15 2023

Keywords

• sign

Links

• Winston de Greef, Table of n, a(n) for n = 0..431
• Eric Weisstein's World of Mathematics, Lambert W-Function.

Crossrefs

Cf. A362276, A362304, A362320.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(lambertw(x^4)^(1/4))/(1+lambertw(x^4))))

Formula

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

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