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A012791 arctanh(sec(x)*arcsin(x))=x+6/3!*x^3+148/5!*x^5+9184/7!*x^7... 0

%I #7 Feb 05 2015 15:23:54

%S 1,6,148,9184,1066640,199000736,54431471040,20523724218880,

%T 10203766053312768,6467780044492713472,5090997086675585360896,

%U 4871968356294907783585792,5570589015199967686042095616

%N arctanh(sec(x)*arcsin(x))=x+6/3!*x^3+148/5!*x^5+9184/7!*x^7...

%F a(n) ~ (2*n)! / r^(2*n+1), where r = 0.6948196907307875655784200727751937626855... is the root of the equation sec(r)*arcsin(r) = 1. - _Vaclav Kotesovec_, Feb 05 2015

%t nn = 20; Table[(CoefficientList[Series[ArcTanh[ArcSin[x]*Sec[x]], {x, 0, 2*nn+1}], x] * Range[0, 2*nn+1]!)[[n]], {n, 2, 2*nn, 2}] (* _Vaclav Kotesovec_, Feb 05 2015 *)

%K nonn

%O 0,2

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

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