A375879 E.g.f. satisfies A(x) = 1/(1 - x)^(3*A(x)^(1/3)).

1, 3, 18, 159, 1860, 27180, 477702, 9830814, 232182024, 6195709008, 184478436720, 6066613989216, 218468134274904, 8553367426018896, 361834389120925224, 16450660929420051480, 800070438821317486272, 41453084674400350385664

Offset: 0

Author

Seiichi Manyama, Sep 01 2024

Keywords

• nonn
• changed

Links

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

Crossrefs

Cf. A052813, A375878.

Programs

PARI

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

PARI

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

Formula

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A052813.

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

a(n) = 3 * Sum_{k=0..n} (k+3)^(k-1) * |Stirling1(n,k)|.

a(n) ~ 3 * n^(n-1) * exp(7/2 + n*exp(-1) - n) / (exp(exp(-1)) - 1)^(n - 1/2). - Vaclav Kotesovec, Aug 27 2025