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%I #7 Feb 05 2015 15:34:18
%S 1,6,140,8456,957840,174293856,46514037440,17115342333056,
%T 8304761365213440,5137820023434733056,3947233200665413667840,
%U 3686931444647916864505856,4114664615209642258282352640
%N arctanh(sec(x)*sinh(x))=x+6/3!*x^3+140/5!*x^5+8456/7!*x^7...
%F a(n) ~ (2*n)! / r^(2*n+1), where r = 0.7032906588639654058999212003816567397131... is the root of the equation sec(r)*sinh(r) = 1. - _Vaclav Kotesovec_, Feb 05 2015
%t nn = 20; Table[(CoefficientList[Series[ArcTanh[Sec[x]*Sinh[x]], {x, 0, 2*nn+1}], x] * Range[0, 2*nn+1]!)[[n]], {n, 2, 2*nn, 2}] (* _Vaclav Kotesovec_, Feb 05 2015 *)
%K nonn
%O 0,2
%A Patrick Demichel (patrick.demichel(AT)hp.com)
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