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Arcsinh(arctan(x)^2) = 2/2!*x^2 - 16/4!*x^4 + 248/6!*x^6 - 3456/8!*x^8 + ...
1

%I #13 Jan 09 2024 13:20:30

%S 0,2,-16,248,-3456,-164448,17537280,5001348480,-3047690956800,

%T 999150768960000,-194340969261158400,-28292890791044597760,

%U 48811395838790000148480,-15658656394130132870062080,-19215487887156327014813859840,37972554002174500707798919249920

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

%t With[{nn=30},Take[CoefficientList[Series[ArcSinh[ArcTan[x]^2],{x,0,nn}],x] Range[0,nn]!,{1,-1,2}]] (* _Harvey P. Dale_, May 06 2013 *)

%K sign

%O 0,2

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

%E Definition clarified by _Harvey P. Dale_, May 06 2013