A362173 a(n) = n! * Sum_{k=0..floor(n/3)} (n/6)^k * binomial(n-2*k,k)/(n-2*k)!.

1, 1, 1, 4, 17, 51, 481, 3676, 18369, 272917, 3011201, 21058236, 427112401, 6160655359, 55380250017, 1423658493076, 25361574327041, 278603741558601, 8673295084155649, 183914415577719892, 2387417408385462801, 87273239189497636171, 2146479566819857007201

Offset: 0

Author

Seiichi Manyama, Apr 14 2023

Keywords

• nonn

Links

• Winston de Greef, Table of n, a(n) for n = 0..441
• Eric Weisstein's World of Mathematics, Lambert W-Function.

Crossrefs

Main diagonal of A362043.

Cf. A277614, A362300, A362301.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((-2*lambertw(-x^3/2))^(1/3))/(1+lambertw(-x^3/2))))

Formula

a(n) = n! * [x^n] exp(x + n*x^3/6).

E.g.f.: exp( ( -2*LambertW(-x^3/2) )^(1/3) ) / (1 + LambertW(-x^3/2)).