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%I #8 Jul 16 2014 16:40:52
%S 0,1,2,6,32,280,3192,43344,690496,12726144,266222880,6222163200,
%T 160658284800,4542751030272,139616399952512,4634016219678720,
%U 165191949394008064,6294553527003086848,255316547059075256832
%N E.g.f. satisfies: A(x) = x*(sinh(sinh(A(x)))+1).
%H Alois P. Heinz, <a href="/A133596/b133596.txt">Table of n, a(n) for n = 0..100</a>
%F a(n) ~ n^(n-1) * sqrt(s/((s-r)*(cosh(s))^2 + tanh(s))) / (exp(n) * r^n), where r = 0.4068975138196165625... and s = 0.9455473915228318233... are roots of the system of equations r*cosh(s)*cosh(sinh(s)) = 1, s = r + r*sinh(sinh(s)). - _Vaclav Kotesovec_, Jul 16 2014
%p A:= proc(n) option remember; if n=0 then 0 else convert (series (x* (sinh (sinh(A(n-1)))+1), x=0, n+1), polynom) fi end: a:= n-> coeff (A(n), x, n)*n!: seq (a(n), n=0..23);
%t CoefficientList[InverseSeries[Series[x/(1 + Sinh[Sinh[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
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