A012457 sin(arctan(x)^2)=2/2!*x^2-16/4!*x^4+248/6!*x^6-3456/8!*x^8...

2, -16, 248, -3456, -406368, 123982080, -31807263360, 9173875200000, -3114459024453120, 1251070155460915200, -591321674803999426560, 326012628782956574638080, -207713640106463567695994880

Offset: 0

Author

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

Keywords

• sign

Links

• Robert Israel, Table of n, a(n) for n = 0..223

Programs

Maple

S:= series(g,x,52):
seq(coeff(S,x,2*j)*(2*j)!,j=1..25); # Robert Israel, Apr 04 2016

Mathematica

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 *)

Formula

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

Extensions

Definition clarified by Harvey P. Dale, Aug 20 2014