A362705 -id:A362705 - cp's OEIS frontend

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

Seiichi Manyama, Apr 30 2023

nonn

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

Cf. A072034, A362700.

Cf. A362705.

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

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

A362704 Expansion of e.g.f. 1/(1 + LambertW(-x^2/2 * exp(x))).

Original entry on oeis.org

1, 0, 1, 3, 18, 130, 1140, 11886, 142408, 1934640, 29357100, 492249340, 9038206056, 180352513848, 3886286296984, 89937276717120, 2224716791224320, 58577968147130176, 1635780290409117648, 48286974141713673072, 1502385897082471446880

Offset: 0

Seiichi Manyama, Apr 30 2023

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

Cf. A072034, A362705.

Cf. A362350.

my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+lambertw(-x^2/2*exp(x)))))

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

cp's OEIS Frontend

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

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