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%I #9 Nov 28 2016 20:53:45
%S 2,13,553,57839,11359153,3579398359,1655031037177,1054978773554159,
%T 886822655405158113,950463966040325692455,1265021553451798971633001,
%U 2047001827823001219625900543,3957634961967849174268972586001
%N arctanh(arctan(x)+sin(x))=2*x+13/3!*x^3+553/5!*x^5+57839/7!*x^7...
%F a(n) ~ (2*n)! / r^(2*n+1), where r = 0.5343315247229429263511748056113294391694... is the root of the equation arctan(r)+sin(r) = 1. - _Vaclav Kotesovec_, Feb 05 2015
%t nn = 20; Table[(CoefficientList[Series[ArcTanh[ArcTan[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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