A013410 - OEIS

%I #14 Mar 25 2013 21:37:41

%S 0,3,-15,945,-44415,5769225,-711485775,171504558225,-40549611477375,

%T 15553976334521625,-6025672551378855375,3368007502842396038625,

%U -1937899053877871819109375,1488068350680083972290115625

%N Coefficient of x^(2n+1)/(2n+1)! in arctan(arcsin(x)-arctan(x))=3/3!*x^3-15/5!*x^5+945/7!*x^7-44415/9!*x^9...

%t With[{nn=30},Take[CoefficientList[Series[ArcTan[ArcSin[x]-ArcTan[x]],{x,0,nn}],x] Range[0,nn-1]!,{4,-1,2}]] (* _Harvey P. Dale_, Mar 25 2013 *)

%o (PARI) A013410(n)=x='x+O('x^(2*n+2));polcoeff(atan(asin(x)-atan(x)),2*n+1)*(n*2+1)!

%K sign

%O 0,2

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

%E Definition clarified by _Harvey P. Dale_ and _M. F. Hasler_, initial term a(0)=0 added as suggested by _N. J. A. Sloane_, Mar 25 2013