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sech(arctan(arcsin(x)))=1-1/2!*x^2+9/4!*x^4-249/6!*x^6+11953/8!*x^8...
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%I #6 Apr 08 2018 21:20:56

%S 1,-1,9,-249,11953,-992401,115133433,-19289685193,4104153335777,

%T -1154213252748193,390283459641717353,-165544701587974757145,

%U 81456402896849322863505,-48584594120969426596224305

%N sech(arctan(arcsin(x)))=1-1/2!*x^2+9/4!*x^4-249/6!*x^6+11953/8!*x^8...

%t With[{nn=30},Take[CoefficientList[Series[Sech[ArcTan[ArcSin[x]]],{x,0,nn}],x] Range[0,nn]!,{1,-1,2}]] (* _Harvey P. Dale_, Apr 08 2018 *)

%K sign

%O 0,3

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