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sin(arctan(x)^2)=2/2!*x^2-16/4!*x^4+248/6!*x^6-3456/8!*x^8...
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%I #10 Apr 04 2016 23:19:17

%S 2,-16,248,-3456,-406368,123982080,-31807263360,9173875200000,

%T -3114459024453120,1251070155460915200,-591321674803999426560,

%U 326012628782956574638080,-207713640106463567695994880

%N sin(arctan(x)^2)=2/2!*x^2-16/4!*x^4+248/6!*x^6-3456/8!*x^8...

%H Robert Israel, <a href="/A012457/b012457.txt">Table of n, a(n) for n = 0..223</a>

%F Sum_{n>=0} a(n) x^(2*n+2)/(2*n+2)! = sin(arctan(x)^2). - _Robert Israel_, Apr 04 2016

%p S:= series(g,x,52):

%p seq(coeff(S,x,2*j)*(2*j)!,j=1..25); # _Robert Israel_, Apr 04 2016

%t With[{nn=30},Take[CoefficientList[Series[Sin[ArcTan[x]^2],{x,0,nn}],x] Range[0,nn]!,{3,-1,2}]] (* _Harvey P. Dale_, Aug 20 2014 *)

%K sign

%O 0,1

%A Patrick Demichel (patrick.demichel(AT)hp.com)

%E Definition clarified by _Harvey P. Dale_, Aug 20 2014