A012297 Expansion of e.g.f. arctan(sin(x)*sin(x)), even powers only.

2, -8, -208, 13312, 161792, -138042368, 9993992192, 4147254525952, -1386315007787008, -171033573395529728, 284350624150760456192, -45336566464274820497408, -87136608072231186709086208

Offset

0,1

Links

G. C. Greubel, Table of n, a(n) for n = 0..222

Example

E.g.f. = 2*x^2/2! - 8*x^4/4! - 208*x^6/6! + 13312*x^8/8! + ...

Mathematica

With[{nn = 40}, CoefficientList[Series[ArcTan[Sin[x]^2], {x, 0, nn}], x] Range[0, nn]!][[1 ;; ;; 2]] (* G. C. Greubel, Oct 26 2018 *)

Prog

(PARI) x='x+O('x^40); v=Vec(serlaplace(atan(sin(x)^2))); vector(#v\2, n, v[2*n-1]) \\ G. C. Greubel, Oct 26 2018
(Magma) m:=40; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Arctan(Sin(x)^2) ));  [Factorial(2*n+2)*b[2*n+1]: n in [0..Floor((m-4)/2)]];  // G. C. Greubel, Oct 26 2018

Crossrefs

Sequence in context: A012535 A012300 A009801 * A000893 A030177 A009611

Adjacent sequences: A012294 A012295 A012296 * A012298 A012299 A012300

Keyword

sign

Author

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

Status

approved