A362705 Expansion of e.g.f. 1/(1 + LambertW(-x^3/6 * exp(x))).

1, 0, 0, 1, 4, 10, 60, 595, 4536, 34524, 361320, 4333725, 51214460, 651628406, 9448719644, 146868322055, 2376666773040, 41077757951000, 762599081332176, 14918668387075449, 305774990501285940, 6602482711971622210, 149921553418087172260, 3557552268845721893131

Offset: 0

Author

Seiichi Manyama, Apr 30 2023

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A072034, A362704.

Cf. A362351.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+lambertw(-x^3/6*exp(x)))))

Formula

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