login
arctanh(arcsinh(x)*cos(x))=x-2/3!*x^3-32/5!*x^5+152/7!*x^7+48448/9!*x^9...
0

%I #9 Nov 01 2013 05:36:22

%S 1,-2,-32,152,48448,289408,-393649024,-34249082624,12871254335488,

%T 2591959365570560,-694262452828553216,-534293242711984668672,

%U 97599429997759939117056,140451121892184627503628288

%N arctanh(arcsinh(x)*cos(x))=x-2/3!*x^3-32/5!*x^5+152/7!*x^7+48448/9!*x^9...

%F a(n) ~ (-1)^n * cosh(1) * 2^(2*n+3) * n^(2*n) / ((4+Pi^2*cosh(1)^2) * exp(2*n)). - _Vaclav Kotesovec_, Nov 01 2013

%t With[{nn=30},Take[CoefficientList[Series[ArcTanh[ArcSinh[x]Cos[x]],{x,0,nn}],x]Range[0,nn-1]!,{2,-1,2}]] (* _Harvey P. Dale_, Oct 20 2012 *)

%K sign

%O 0,2

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