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%I #10 Feb 04 2015 17:59:15
%S 1,-6,120,-6216,548544,-74860544,14571230336,-3827313412352,
%T 1304171528695808,-559299942314340352,294737591597024591872,
%U -187195194238509459439616,141014910901971840963870720
%N tanh(arcsinh(x)*cos(x))=x-6/3!*x^3+120/5!*x^5-6216/7!*x^7...
%H Vaclav Kotesovec, <a href="/A012641/b012641.txt">Table of n, a(n) for n = 0..218</a>
%F a(n) ~ c * (-1)^n * (2*n)! * n / r^(2*n), where r = 0.8922083063567712426146182695087047187586345275404... is the root of the equation arcsin(r)*cosh(r) = Pi/2, c = 1.175488110258... . - _Vaclav Kotesovec_, Feb 04 2015
%t nn = 20; Table[(CoefficientList[Series[Tanh[ArcSinh[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)