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tan(arctanh(x)*tanh(x))=2/2!*x^2+400/6!*x^6+2688/8!*x^8...
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%I #8 Feb 06 2015 11:10:13

%S 0,2,0,400,2688,1631488,60938240,35243972608,3826154307584,

%T 2477263324839936,571708399442198528,435722170330996801536,

%U 177081722613295659089920,162107313371111569999527936

%N tan(arctanh(x)*tanh(x))=2/2!*x^2+400/6!*x^6+2688/8!*x^8...

%F a(n) ~ (2*n)! * sinh(2*r) / ((Pi/2 + (sinh(r))^2/(1-r^2)) * r^(2*n+1)), where r = 0.970313828446324195188532490988552661547225320103102781254845... is the root of the equation arctanh(r)*tanh(r) = Pi/2. - _Vaclav Kotesovec_, Feb 06 2015

%t nn = 20; Table[(CoefficientList[Series[Tan[ArcTanh[x]*Tanh[x]], {x, 0, 2*nn}], x] * Range[0, 2*nn]!)[[n]], {n, 1, 2*nn+1, 2}] (* _Vaclav Kotesovec_, Feb 06 2015 *)

%K nonn

%O 0,2

%A Patrick Demichel (patrick.demichel(AT)hp.com)

%E a(0)=0 prepended by _Vaclav Kotesovec_, Feb 06 2015