A362703 Expansion of e.g.f. 1/(1 + LambertW(-x^3 * exp(x))).

1, 0, 0, 6, 24, 60, 1560, 20370, 161616, 2601144, 53827920, 829605150, 14894289960, 360575394036, 8234733389064, 188800085076330, 5145737430116640, 148419618327231600, 4278452209330445856, 134018446273097264694, 4529883358179857555640

Offset: 0

Author

Seiichi Manyama, Apr 30 2023

Keywords

• nonn
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..414
• Eric Weisstein's World of Mathematics, Lambert W-Function.

Crossrefs

Cf. A072034, A362702.

Cf. A292889, A362348, A362699.

Programs

PARI

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

Formula

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