A375877 E.g.f. satisfies A(x) = exp( 3 * (exp(x) - 1) * A(x)^(1/3) ).

1, 3, 18, 156, 1785, 25506, 438540, 8834013, 204341580, 5343030264, 155949552951, 5028857184588, 177628447077408, 6822752257361943, 283211285330197254, 12636574861035192648, 603220473535136763441, 30679940004725753797230

Offset: 0

Author

Seiichi Manyama, Sep 01 2024

Keywords

• nonn

Links

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

Crossrefs

Cf. A052880, A375876.

Programs

PARI

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

PARI

a(n) = 3*sum(k=0, n, (k+3)^(k-1)*stirling(n, k, 2));

Formula

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A052880.

E.g.f.: exp( - 3*LambertW(1 - exp(x)) ).

a(n) = 3 * Sum_{k=0..n} (k+3)^(k-1) * Stirling2(n,k).