%I #11 Jul 16 2014 15:42:34
%S 0,1,2,9,68,735,10332,178276,3639680,85750461,2289322710,68298539441,
%T 2251768422840,81301875813340,3190478732975744,135209859332836905,
%U 6154229137942791184,299422872446882413387,15507211446546229257948
%N E.g.f. satisfies: A(x) = x*(sinh(exp(A(x))-1)+1).
%H Alois P. Heinz, <a href="/A134261/b134261.txt">Table of n, a(n) for n = 0..100</a>
%F a(n) ~ n^(n-1) * sqrt(s/(1+exp(2*s)*(s-r))) / (exp(n)*r^n), where r = 0.3186838609215673947... and s = 0.6997097688577272466... are roots of the system of equations s+r*sinh(1-exp(s))=r, exp(s)*r*cosh(1-exp(s))=1. - _Vaclav Kotesovec_, Jul 16 2014
%p A:= proc(n) option remember; if n=0 then 0 else convert (series (x* (sinh (exp(A(n-1))-1)+1), x=0, n+1), polynom) fi end: a:= n-> coeff (A(n), x, n)*n!: seq (a(n), n=0..22);
%t CoefficientList[InverseSeries[Series[-(x/(-1 + Sinh[1 - E^x])),{x,0,20}],x],x] * Range[0,20]! (* _Vaclav Kotesovec_, Jul 16 2014 *)
%K nonn
%O 0,3
%A _Alois P. Heinz_, Aug 27 2008