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%I #10 Feb 04 2015 17:46:22
%S 1,-2,28,-520,59728,-3842720,963273920,-151564390016,60786495498496,
%T -18563464667034112,10709479914780654592,-5442000735745663911936,
%U 4284121800522638439469056,-3262273090906052050909765632
%N arcsinh(arctanh(x)*cos(x))=x-2/3!*x^3+28/5!*x^5-520/7!*x^7+59728/9!*x^9...
%H Vaclav Kotesovec, <a href="/A012745/b012745.txt">Table of n, a(n) for n = 0..218</a>
%F a(n) ~ c * (-1)^n * (2*n)! / (sqrt(n) * r^(2*n)), where r = 0.867011256808704179615963011549544766868066027225... is the root of the equation arctan(r)*cosh(r) = 1, c = 0.741862954403555... . - _Vaclav Kotesovec_, Feb 04 2015
%t nn = 20; Table[(CoefficientList[Series[ArcSinh[ArcTanh[x]*Cos[x]], {x, 0, 2*nn+1}], x] * Range[0, 2*nn+1]!)[[n]], {n, 2, 2*nn, 2}] (* _Vaclav Kotesovec_, Feb 04 2015 *)
%K sign
%O 0,2
%A Patrick Demichel (patrick.demichel(AT)hp.com)