A362702 Expansion of e.g.f. 1/(1 + LambertW(-x^2 * exp(x))).

1, 0, 2, 6, 60, 500, 6150, 81522, 1300376, 23024808, 459915210, 10104914270, 243652575012, 6378414900156, 180405368976014, 5478759958122570, 177868544365861680, 6146407749811022672, 225262698504062963346, 8727083181657584963766

Offset: 0

Author

Seiichi Manyama, Apr 30 2023

Keywords

• nonn
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..401
• Eric Weisstein's World of Mathematics, Lambert W-Function.

Crossrefs

Cf. A072034, A362703.

Cf. A216507, A362347.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1+lambertw(-x^2*exp(x)))))

Formula

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