A362699 -id:A362699 - cp's OEIS frontend

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

Seiichi Manyama, Apr 30 2023

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

Cf. A072034, A362702.

Cf. A292889, A362348, A362699.

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

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

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

Original entry on oeis.org

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

Offset: 0

Seiichi Manyama, Apr 30 2023

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

Cf. A072034, A362699.

Cf. A216688, A356834, A362700, A362702.

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

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

cp's OEIS Frontend

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

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