A362340 a(n) = n! * Sum_{k=0..floor(n/2)} (-k/2)^k / (k! * (n-2*k)!).

1, 1, 0, -2, 7, 51, -239, -2435, 16353, 209377, -1826099, -28232379, 303020125, 5494172893, -70032035163, -1457369472299, 21512472563281, 505400696581905, -8478758871011807, -221971772323923263, 4171251104170567101, 120416449897739144941

Offset: 0

Author

Seiichi Manyama, Apr 17 2023

Keywords

• sign

Links

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

Crossrefs

Cf. A069856, A362341, A362342.

Cf. A362276.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x)/(1+lambertw(x^2/2))))

Formula

E.g.f.: exp(x) / (1 + LambertW(x^2/2)).