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Expansion of arcsin(sinh(x)*sinh(x)).
2

%I #13 Feb 16 2017 03:20:30

%S 0,2,8,152,6848,554912,70690688,13009484672,3265063958528,

%T 1071643508306432,445538702940858368,228823524775428872192,

%U 142264706412727018078208,105297877340452669962493952

%N Expansion of arcsin(sinh(x)*sinh(x)).

%H G. C. Greubel, <a href="/A012571/b012571.txt">Table of n, a(n) for n = 0..220</a>

%F a(n) ~ (2*n)! / (2^(1/4) * sqrt(Pi) * n^(3/2) * (log(1+sqrt(2)))^(2*n-1/2)). - _Vaclav Kotesovec_, Feb 06 2015

%e arcsin(sinh(x)*sinh(x)) = 2/2!*x^2+8/4!*x^4+152/6!*x^6+6848/8!*x^8...

%t With[{nn=30},Take[CoefficientList[Series[ArcSin[Sinh[x]^2],{x,0,nn}],x] Range[0,nn]!,{1,-1,2}]] (* _Harvey P. Dale_, Dec 11 2013 *)

%Y Appears to equal 2 * A012101.

%K nonn

%O 0,2

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

%E a(0)=0 prepended by _Vaclav Kotesovec_, Feb 06 2015