A362342 a(n) = n! * Sum_{k=0..floor(n/4)} (-k/24)^k / (k! * (n-4*k)!).

1, 1, 1, 1, 0, -4, -14, -34, 71, 1135, 6091, 22771, -87119, -1847559, -13769755, -70046339, 390688481, 10473961121, 100030347361, 643972996705, -4717305354419, -153449916040259, -1787926183752939, -13926752488607419, 126329848106764765

Offset: 0

Author

Seiichi Manyama, Apr 17 2023

Keywords

• sign

Links

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

Crossrefs

Cf. A069856, A362340, A362341.

Cf. A351930, A362345, A362349.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x)/(1+lambertw(x^4/24))))

Formula

E.g.f.: exp(x) / (1 + LambertW(x^4/24)).