A355782 E.g.f. satisfies log(A(x)) = 2 * (1 - exp(-x)) * A(x).

1, 2, 10, 94, 1314, 24494, 572418, 16109678, 530772610, 20049256686, 854425665410, 40560727143534, 2122785621956226, 121440903560075246, 7539867236251002242, 504946360197545803630, 36284349255747713008770, 2784785703026225861819118

Offset

0,2

Links

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

Formula

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

a(n) = Sum_{k=0..n} (-1)^(n-k) * 2^k * (k+1)^(k-1) * Stirling2(n,k).

From Vaclav Kotesovec, Jul 18 2022: (Start)

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

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

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(2*(exp(-x)-1)))))
(PARI) a(n) = sum(k=0, n, (-1)^(n-k)*2^k*(k+1)^(k-1)*stirling(n, k, 2));

Crossrefs

Cf. A058864, A351277, A355789.

Sequence in context: A026025 A231375 A100622 * A103436 A182173 A362643

Adjacent sequences: A355779 A355780 A355781 * A355783 A355784 A355785

Keyword

nonn

Author

Seiichi Manyama, Jul 16 2022

Status

approved