A355786 E.g.f. satisfies A(x) = 1/(1 - 2*x)^(A(x)/2).

1, 1, 5, 42, 497, 7620, 143979, 3241406, 84847489, 2534788296, 85170416115, 3180919433802, 130771002469953, 5869920100483452, 285705285804636411, 14989889385040915830, 843420165009747027969, 50664760467069168337680, 3236433107379299238343779

Offset: 0

Author

Seiichi Manyama, Jul 17 2022

Keywords

• nonn

Crossrefs

Cf. A052813, A355779.

Programs

PARI

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

PARI

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

Formula

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

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

From Vaclav Kotesovec, Jul 18 2022: (Start)

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

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