A012989 Expansion of e.g.f. cos(arctan(x) + arcsin(x)) = ((1-x^2)^(1/2) - x^2)/(1+x^2)^(1/2), even powers only.

1, -4, 24, -630, 27720, -2353050, 267567300, -46909412550, 10103827734000, -3007951147451250, 1049953727680357500, -474655168783984938750, 244316469166238814345000, -155979504015802517206406250

Offset

0,2

Links

Table of n, a(n) for n=0..13.

Example

((1-x^2)^(1/2) - x^2)/(1+x^2)^(1/2) = 1 - (4/2!)*x^2 + (24/4!)*x^4 - (630/6!)*x^6 + (27720/8!)*x^8 ...

Mathematica

mx = 13; Delete[ Range[0, 2 mx]! CoefficientList[ Series[ (Sqrt[1 - x^2] - x^2)/Sqrt[1 + x^2], {x, 0, 2 mx}], x], Split[2 Range@ mx]] (* Robert G. Wilson v, Oct 22 2012 *)
With[{nn=30}, Take[CoefficientList[Series[Cos[ArcTan[x]+ArcSin[x]], {x, 0, nn}], x] Range[0, nn]!, {1, -1, 2}]] (* Harvey P. Dale, Dec 12 2018 *)

Crossrefs

Sequence in context: A216092 A174245 A228191 * A347480 A058171 A196866

Adjacent sequences: A012986 A012987 A012988 * A012990 A012991 A012992

Keyword

sign

Author

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

Extensions

Name corrected and e.g.f. simplified by Sergei N. Gladkovskii and Joerg Arndt, Oct 23 2012

Status

approved