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%I #7 Feb 05 2015 15:42:52
%S 2,16,778,94064,21203218,7679356144,4079013377242,2987290363267664,
%T 2884950332801855778,3552295906912003762512,5431778247093958269249706,
%U 10097951729467246217104155568
%N arctanh(arcsin(x)+sin(x))=2*x+16/3!*x^3+778/5!*x^5+94064/7!*x^7...
%F a(n) ~ (2*n)! / r^(2*n+1), where r = 0.4985117060766136685059797926558609110334... is the root of the equation arcsin(r)+sin(r) = 1. - _Vaclav Kotesovec_, Feb 05 2015
%t nn = 20; Table[(CoefficientList[Series[ArcTanh[ArcSin[x] + Sin[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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