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%I #9 Feb 07 2015 04:42:24
%S 1,7,185,11471,1263185,215079159,52220520521,17117211436287,
%T 7278847910698529,3895256097472909671,2561265786122546675545,
%U 2029572906879775183011503,1907361016227301624675795825
%N tan(sec(x)*arctanh(x))=x+7/3!*x^3+185/5!*x^5+11471/7!*x^7...
%H Vaclav Kotesovec, <a href="/A012843/b012843.txt">Table of n, a(n) for n = 0..200</a>
%H Vaclav Kotesovec, <a href="/A012843/a012843.jpg">Graph - abs(e.g.f.) in the complex plane</a>
%F a(n) ~ 4 * cos(r) * (2*n+1)! / ((2/(1-r^2) + Pi*sin(r)) * r^(2*n+2)), where r = 0.7989151684962902269091787502961348455829847186615330217492... is the root of the equation sec(r)*arctanh(r) = Pi/2. - _Vaclav Kotesovec_, Feb 07 2015
%t nn = 20; Table[(CoefficientList[Series[Tan[ArcTanh[x]*Sec[x]], {x, 0, 2*nn+1}], x] * Range[0, 2*nn+1]!)[[n]], {n, 2, 2*nn, 2}] (* _Vaclav Kotesovec_, Feb 07 2015 *)
%K nonn
%O 0,2
%A Patrick Demichel (patrick.demichel(AT)hp.com)