A355787 E.g.f. satisfies A(x) = (1 + 2*x)^(A(x)/2).

1, 1, 1, 6, 17, 220, 939, 20930, 107393, 3823416, 20382195, 1147905462, 5519388225, 515034742404, 1817577994491, 323878306632330, 481078381979649, 272556878473903344, -355395800536648605, 296393140746445749246, -1420979986049970526335

Offset: 0

Author

Seiichi Manyama, Jul 17 2022

Keywords

• sign

Crossrefs

Cf. A033917, A355780.

Programs

PARI

my(N=30, 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)*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).