A355779 E.g.f. satisfies A(x) = 1/(1 - x)^(2 * A(x)).

1, 2, 14, 168, 2912, 66600, 1900056, 65101120, 2606993728, 119561789952, 6181730106240, 355838533286016, 22573258090527360, 1564818434983235328, 117698836976753297664, 9547346757806586746880, 830846347686871026714624, 77215374643802544102187008

Offset: 0

Author

Seiichi Manyama, Jul 16 2022

Keywords

• nonn

Crossrefs

Cf. A052813, A351275, A355786.

Programs

PARI

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

PARI

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

Formula

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

a(n) = Sum_{k=0..n} 2^k * (k+1)^(k-1) * |Stirling1(n,k)|.

From Vaclav Kotesovec, Jul 18 2022: (Start)

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

a(n) ~ sqrt(2) * n^(n-1) * exp(3/2 - n + n*exp(-1)/2) / (exp(exp(-1)/2) - 1)^(n - 1/2). (End)