A009324 Expansion of e.g.f. log(1+log(1+x)/exp(x)).

0, 1, -4, 19, -125, 1083, -11669, 150512, -2262546, 38851957, -750394759, 16102118954, -380058372572, 9785829784651, -272962664838317, 8199582838569366, -263901999580713904, 9059869807873906105

Offset: 0

Author

R. H. Hardin

Keywords

• sign
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 173

Programs

Mathematica

With[{nn=20},CoefficientList[Series[Log[1+Log[1+x]/Exp[x]],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Jun 22 2013 *)

Formula

a(n) ~ (n-1)! * (-1)^(n+1) / r^n, where r = 0.46605913165918886499866250745716312978322387778... is the root of the equation exp(exp(-r))*(1-r) = 1. - Vaclav Kotesovec, Jan 24 2015

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Previous Mathematica program replaced and Definition clarified by Harvey P. Dale, Jun 22 2013