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%I #8 Jun 12 2017 18:30:49
%S 1,1,9,57,5169,-93807,31981689,-3857766903,1058896281825,
%T -286891166986335,108826313005021545,-47766338018402914215,
%U 25721485923005221938705,-16179153687877979599066575
%N tan(arcsin(arctan(x)))=x+1/3!*x^3+9/5!*x^5+57/7!*x^7+5169/9!*x^9...
%F a(n)=(2*n+1)!*sum(m=0..n, binomial(2*m,m)*2^(-4*m-1)*(2*m+1)!*(-1)^(n+m)*sum(i=2*m+1..2*n+1, (2^i*stirling1(i,2*m+1)*binomial(2*n,i-1))/i!)). [Vladimir Kruchinin, Jun 15 2011]
%t With[{nn=30},Take[CoefficientList[Series[Tan[ArcSin[ArcTan[x]]],{x,0,nn}],x] Range[0,nn-1]!,{2,-1,2}]] (* _Harvey P. Dale_, Jun 12 2017 *)
%o (Maxima)
%o a(n):=(2*n+1)!*sum(binomial(2*m,m)*2^(-4*m-1)*(2*m+1)!*(-1)^(n+m)*sum((2^i*stirling1(i,2*m+1)*binomial(2*n,i-1))/i!,i,2*m+1,2*n+1),m,0,n); [Vladimir Kruchinin, Jun 15 2011]
%K sign
%O 0,3
%A Patrick Demichel (patrick.demichel(AT)hp.com)
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