A362604 Expansion of e.g.f. 1/(1 + LambertW(-x * exp(x^2))).

1, 1, 4, 33, 352, 4805, 80256, 1582693, 36001792, 927974601, 26729943040, 850921057481, 29666297020416, 1124166449205709, 46005243970846720, 2022121401647311245, 95008417631810093056, 4751844218849365365137, 252063937292253895065600

Offset: 0

Author

Seiichi Manyama, Apr 30 2023

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A072034, A362699.

Cf. A216688, A356834, A362700, A362702.

Programs

PARI

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

Formula

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