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%I #8 Feb 06 2015 10:33:05
%S 0,2,12,430,27384,2844538,444855620,96566466022,27798112443248,
%T 10239758940342642,4695120560496345596,2621628020059813754526,
%U 1751011006876497963996520,1378272807335260827405511146
%N tan(arctanh(x)*sinh(x))=2/2!*x^2+12/4!*x^4+430/6!*x^6+27384/8!*x^8...
%F a(n) ~ 4*(1-r^2) * (2*n)! / (((1-r^2)*Pi/tanh(r) + 2*sinh(r)) * r^(2*n+1)), where r = 0.907648090497239832680442727614114269985280667634413195506087... is the root of the equation arctanh(r)*sinh(r) = Pi/2. - _Vaclav Kotesovec_, Feb 06 2015
%t nn = 20; Table[(CoefficientList[Series[Tan[ArcTanh[x]*Sinh[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