A362276 a(n) = n! * Sum_{k=0..floor(n/2)} (-n/2)^k * binomial(n-k,k)/(n-k)!.

1, 1, -1, -8, 25, 326, -1709, -31016, 228257, 5311900, -50337449, -1429574464, 16573668409, 555724876552, -7619288730325, -294582728145824, 4662562423032961, 204200579987319824, -3664348770051277073, -179294278761195862400, 3597007651803106610201

Offset: 0

Author

Seiichi Manyama, Apr 13 2023

Keywords

• sign

Links

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

Crossrefs

Main diagonal of A362277.

Cf. A277614.

Programs

PARI

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

Formula

a(n) = n! * [x^n] exp(x - n*x^2/2).

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