A362859 Expansion of e.g.f. exp(-x) / (1 + LambertW(-2*x)).

1, 1, 13, 173, 3321, 81529, 2443333, 86475493, 3529941873, 163260749681, 8437633695741, 481912844592541, 30142773978386281, 2049173019206244073, 150443505029536707381, 11862692305729094644949, 999864950902004743707873, 89709634016056661732903137

Offset: 0

Author

Seiichi Manyama, May 05 2023

Keywords

• nonn
• easy

Links

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

Crossrefs

Column k=2 of A362019.

Cf. A062971, A362857.

Programs

PARI

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

Formula

G.f.: Sum_{k>=0} (2*k*x)^k / (1 + x)^(k+1).

a(n) = (-1)^n * Sum_{k=0..n} (-2*k)^k * binomial(n,k).