A099391 Expansion of e.g.f. 1/(2 - exp(exp(exp(x) - 1) - 1)).

1, 1, 5, 36, 342, 4048, 57437, 950512, 17975438, 382424397, 9039989107, 235062317196, 6667866337309, 204905200542916, 6781157167505291, 240446179599065951, 9094120016963808935, 365453749501228063845

Offset

0,3

Links

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

K. A. Penson, P. Blasiak, G. Duchamp, A. Horzela and A. I. Solomon, Hierarchical Dobinski-type relations via substitution and the moment problem [J. Phys. A 37 (2004), 3475-3487]

Formula

(1/2) Sum[k=0..inf, k^n/k! * Sum[r=1..inf, e^(-r)r^k/r!*Li(-r, 1/2e) ]], with Li the polylogarithm.

a(n) ~ n! / (2 * (1 + log(2)) * (1 + log(1 + log(2))) * log(1 + log(1 + log(2)))^(n+1)). - Vaclav Kotesovec, Jun 26 2022

a(n) = Sum_{k=0..n} Stirling2(n,k) * A083355(k). - Seiichi Manyama, May 12 2023

Mathematica

With[{nn=20}, CoefficientList[Series[1/(2-Exp[Exp[Exp[x]-1]-1]), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Apr 10 2014 *)

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(2-exp(exp(exp(x)-1)-1)))) \\ Seiichi Manyama, May 12 2023

Crossrefs

Column k=3 of A363007.

Row p=3 of A153278 (for n>=1).

Cf. A000110, A083355, A130410.

Sequence in context: A277610 A261899 A109186 * A008785 A355494 A081918

Adjacent sequences: A099388 A099389 A099390 * A099392 A099393 A099394

Keyword

nonn

Author

Ralf Stephan, Oct 18 2004

Extensions

Definition clarified by Harvey P. Dale, Apr 10 2014

Status

approved