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%I #7 Feb 05 2015 15:57:08
%S 2,19,1033,139697,35245537,14290318777,8497769039329,6967293521417777,
%T 7532911599857139777,10384169309400234051945,
%U 17776358796209666513666881,36997487367543781033857758881
%N arctanh(tan(x)+arcsin(x))=2*x+19/3!*x^3+1033/5!*x^5+139697/7!*x^7...
%F a(n) ~ (2*n)! / r^(2*n+1), where r = 0.4711468334470747286400957442399130911292... is the root of the equation tan(r)+arcsin(r) = 1. - _Vaclav Kotesovec_, Feb 05 2015
%t nn = 20; Table[(CoefficientList[Series[ArcTanh[ArcSin[x] + Tan[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 0,1
%A Patrick Demichel (patrick.demichel(AT)hp.com)
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