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exp(cosh(x)*arctanh(x)) = 1+x+1/2!*x^2+6/3!*x^3+21/4!*x^4+100/5!*x^5...
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%I #9 Oct 24 2013 16:23:02

%S 1,1,1,6,21,100,645,4256,34153,302352,2966505,32245664,380114493,

%T 4879093440,67244074989,996485811712,15717842398417,264232448010496,

%U 4694489063253585,88283645811756544,1744673430747688805

%N exp(cosh(x)*arctanh(x)) = 1+x+1/2!*x^2+6/3!*x^3+21/4!*x^4+100/5!*x^5...

%F a(n) ~ (n-1)! * (2*n)^(cosh(1)/2) / GAMMA(cosh(1)/2). - _Vaclav Kotesovec_, Oct 24 2013

%t CoefficientList[Series[Exp[Cosh[x]*ArcTanh[x]], {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Oct 24 2013 *)

%K nonn

%O 0,4

%A Patrick Demichel (patrick.demichel(AT)hp.com)