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%I #9 Nov 28 2016 20:49:00
%S 1,3,73,2779,260177,32853491,6787498521,1803655970635,660549566885793,
%T 299826162055728355,172107541834064358121,118707937911469881769147,
%U 98574741929922225569568241
%N arctanh(sec(x)*arctan(x))=x+3/3!*x^3+73/5!*x^5+2779/7!*x^7...
%F a(n) ~ (2*n)! / r^(2*n+1), where r = 0.81654122617273381556779185061232051824097... is the root of the equation sec(r)*arctan(r) = 1. - _Vaclav Kotesovec_, Feb 05 2015
%t nn = 20; Table[(CoefficientList[Series[ArcTanh[ArcTan[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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