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arctanh(sinh(x)*arcsin(x))=2/2!*x^2+8/4!*x^4+320/6!*x^6+15808/8!*x^8...
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%I #10 Feb 05 2015 09:34:42

%S 0,2,8,320,15808,1671808,242521600,52294963968,14823920529408,

%T 5496196568825856,2548323017071149056,1453790822661022908416,

%U 997862723859007908085760,812410035086507459409412096

%N arctanh(sinh(x)*arcsin(x))=2/2!*x^2+8/4!*x^4+320/6!*x^6+15808/8!*x^8...

%F a(n) ~ (2*n-1)! / r^(2*n), where r = 0.858737427017558097934130835838437454788... is the root of the equation sinh(r)*arcsin(r) = 1. - _Vaclav Kotesovec_, Feb 05 2015

%t With[{nn=30},Flatten[{0,Take[CoefficientList[Series[ArcTanh[Sinh[x]ArcSin[x]],{x,0,nn}],x] Range[0,nn]!,{3,-1,2}]}]] (* _Harvey P. Dale_, Oct 31 2013 *)

%K nonn

%O 0,2

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

%E Prepended missing a(0)=0 from _Vaclav Kotesovec_, Feb 05 2015