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%I #9 Feb 06 2015 12:57:29
%S 0,3,23,721,55439,5541481,816082343,167874570865,44930591850143,
%T 15238326353365081,6394194823965172727,3248353545402758819489,
%U 1964538978111655728427567,1394689558266289975472153801
%N tan(arctanh(x)-sin(x)) = 3/3!*x^3 + 23/5!*x^5 + 721/7!*x^7 + 55439/9!*x^9...
%F a(n) ~ 2 * (2*n+1)! / ((1/(1-r^2) - cos(r)) * r^(2*n+2)), where r = 0.983784459148349011762868078924370948682732179832779280193598... is the root of the equation arctanh(r)-sin(r) = Pi/2. - _Vaclav Kotesovec_, Feb 06 2015
%t nn = 20; Table[(CoefficientList[Series[Tan[ArcTanh[x] - Sin[x]], {x, 0, 2*nn+1}], x] * Range[0, 2*nn+1]!)[[n]], {n, 2, 2*nn, 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
%E Definition modified by _Vaclav Kotesovec_, Feb 06 2015