|
%I #11 Sep 08 2022 08:44:38
%S 2,-8,-208,13312,161792,-138042368,9993992192,4147254525952,
%T -1386315007787008,-171033573395529728,284350624150760456192,
%U -45336566464274820497408,-87136608072231186709086208
%N Expansion of e.g.f. arctan(sin(x)*sin(x)), even powers only.
%H G. C. Greubel, <a href="/A012297/b012297.txt">Table of n, a(n) for n = 0..222</a>
%e E.g.f. = 2*x^2/2! - 8*x^4/4! - 208*x^6/6! + 13312*x^8/8! + ...
%t With[{nn = 40}, CoefficientList[Series[ArcTan[Sin[x]^2], {x, 0, nn}], x] Range[0, nn]!][[1 ;; ;; 2]] (* _G. C. Greubel_, Oct 26 2018 *)
%o (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
%o (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
%K sign
%O 0,1
%A Patrick Demichel (patrick.demichel(AT)hp.com)
|
