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%I #9 Nov 02 2013 08:03:22
%S 0,2,-12,22,6888,-422998,-19858212,10668149182,-1244673483312,
%T -393680785867438,254550574752219588,-30031176795810056858,
%U -50358282178393089181512,38448631613848702263196922
%N arcsinh(tanh(x)*sin(x))=2/2!*x^2-12/4!*x^4+22/6!*x^6+6888/8!*x^8...
%F Lim sup n->infinity (|a(n)|/(2*n)!)^(1/(2*n)) = 1.0688665046968199... = abs(1/r), where r is the complex root of the equation sin(r)*exp(2*r) - sin(r) + I*exp(2*r) = -I. - _Vaclav Kotesovec_, Nov 02 2013
%t Table[n!*SeriesCoefficient[ArcSinh[Tanh[x]*Sin[x]],{x,0,n}],{n,0,40,2}] (* _Vaclav Kotesovec_, Nov 02 2013 *)
%K sign
%O 0,2
%A Patrick Demichel (patrick.demichel(AT)hp.com)
%E Prepended missing a(0)=0 from _Vaclav Kotesovec_, Nov 02 2013