A362701 Expansion of e.g.f. 1/(1 + LambertW(-x * exp(x^3/6))).

1, 1, 4, 27, 260, 3205, 48276, 859453, 17656696, 411139233, 10700380520, 307819026031, 9698757574716, 332170854765373, 12286858280098780, 488160559069250985, 20732661511284180656, 937357753835195873857, 44948438093966732331984

Offset: 0

Author

Seiichi Manyama, Apr 30 2023

Keywords

• nonn

Links

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

Crossrefs

Cf. A072034, A362700.

Cf. A362705.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1+lambertw(-x*exp(x^3/6)))))

Formula

a(n) = n! * Sum_{k=0..floor(n/3)} (n-3*k)^(n-2*k) / (6^k * k! * (n-3*k)!).