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

0,4

Links

Table of n, a(n) for n=0..20.

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).

Prog

(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));

Crossrefs

Cf. A033917, A355780.

Sequence in context: A209482 A209341 A376134 * A077022 A074923 A093061

Adjacent sequences: A355784 A355785 A355786 * A355788 A355789 A355790

Keyword

sign

Author

Seiichi Manyama, Jul 17 2022

Status

approved