A355786 - OEIS

%I #11 Jul 18 2022 12:22:37

%S 1,1,5,42,497,7620,143979,3241406,84847489,2534788296,85170416115,

%T 3180919433802,130771002469953,5869920100483452,285705285804636411,

%U 14989889385040915830,843420165009747027969,50664760467069168337680,3236433107379299238343779

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

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

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

%F From _Vaclav Kotesovec_, Jul 18 2022: (Start)

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

%F 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)

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

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

%Y Cf. A052813, A355779.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Jul 17 2022