A355780 E.g.f. satisfies A(x) = (1 + x)^(2 * A(x)).

1, 2, 10, 96, 1352, 25400, 597816, 16941568, 561993344, 21372060672, 916910785920, 43817650647936, 2308500130055808, 132941831957885184, 8308594453077321984, 560108109905112238080, 40514005700203717945344, 3129925644058623770173440

Offset

0,2

Links

Table of n, a(n) for n=0..17.

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 17 2022: (Start)

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

a(n) ~ sqrt(2) * n^(n-1) / ((exp(exp(-1)/2) - 1)^(n - 1/2) * exp(n - 3/2 + exp(-1)/4)). (End)

Prog

(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)*stirling(n, k, 1));

Crossrefs

Cf. A033917, A351274, A355787.

Sequence in context: A362643 A160940 A346649 * A193290 A193435 A132572

Adjacent sequences: A355777 A355778 A355779 * A355781 A355782 A355783

Keyword

nonn

Author

Seiichi Manyama, Jul 16 2022

Status

approved