A362700 Expansion of e.g.f. 1/(1 + LambertW(-x * exp(x^2/2))).

1, 1, 4, 30, 304, 3950, 62736, 1177288, 25489024, 625404060, 17149867840, 519779815016, 17253698140416, 622521514670536, 24257636227003648, 1015256151136695840, 45421939756667293696, 2163253599528596482832, 109270502354027312243712

Offset: 0

Author

Seiichi Manyama, Apr 30 2023

Keywords

• nonn

Links

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

Crossrefs

Cf. A072034, A362701.

Programs

PARI

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

Formula

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