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%I #13 Feb 05 2015 09:26:45
%S 0,2,12,430,26040,2903098,482065540,114403718182,36427784932336,
%T 15033693897929202,7796959901543040892,4965936966951067746846,
%U 3810003526358223726689960,3466033186882425920541836586
%N arctanh(tan(x)*arcsin(x))=2/2!*x^2+12/4!*x^4+430/6!*x^6+26040/8!*x^8...
%F a(n) ~ (2*n-1)! / r^(2*n), where r = 0.8121639902962354379596899348276590246... is the root of the equation tan(r)*arcsin(r) = 1. - _Vaclav Kotesovec_, Feb 05 2015
%t With[{nn=30},Flatten[{0,Take[Rest[CoefficientList[Series[ArcTanh[Tan[x] ArcSin[ x]], {x,0,nn}],x]Range[0,nn]!],{2,-1,2}]}]] (* _Harvey P. Dale_, Nov 01 2011 *)
%K nonn
%O 0,2
%A Patrick Demichel (patrick.demichel(AT)hp.com)
%E Prepended missing a(0)=0 from _Vaclav Kotesovec_, Feb 05 2015
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