%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)