A375876 E.g.f. satisfies A(x) = exp( 2 * (exp(x) - 1) * A(x)^(1/2) ).

1, 2, 10, 76, 790, 10494, 170396, 3278174, 73019522, 1850066136, 52577005426, 1657084522790, 57382017574920, 2166149552961970, 88550946187572482, 3897682631534087692, 183810990395243463198, 9246950189455617225622, 494332095588897164709644

Offset: 0

Author

Seiichi Manyama, Sep 01 2024

Keywords

• nonn

Links

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

Crossrefs

Cf. A052880, A375877.

Programs

PARI

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

PARI

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

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A052880.

E.g.f.: exp( - 2*LambertW(1 - exp(x)) ).

a(n) = 2 * Sum_{k=0..n} (k+2)^(k-1) * Stirling2(n,k).

a(n) ~ 2*sqrt(exp(1) + 1) * n^(n-1) / (exp(n-2) * (log(exp(1) + 1)-1)^(n - 1/2)). - Vaclav Kotesovec, Sep 06 2024