%I #8 Aug 18 2016 12:15:22
%S 1,3,3,-2,-9,-9,2,15,15,-2,-21,-21,2,27,27,-2,-33,-33,2,39,39,-2,-45,
%T -45,2,51,51,-2,-57,-57,2,63,63,-2,-69,-69,2,75,75,-2,-81,-81,2,87,87,
%U -2,-93,-93,2,99,99,-2,-105,-105,2,111,111,-2,-117,-117
%N A Chebyshev transform of the odd numbers.
%C A Chebyshev transform of A005408: if A(x) is the g.f. of a sequence, map it to ((1-x^2)/(1+x^2))A(x/(1+x^2)).
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,-3,2,-1).
%F G.f.: (1-x^2)(1+x+x^2)/(1-x+x^2)^2; a(n)=2a(n-1)-3a(n-2)+2a(n-3)-a(n-4); a(n)=n*sum{k=0..floor(n/2), (-1)^k*binomial(n-k, k)*(2(n-2k)+1)/(n-k)}.
%t LinearRecurrence[{2,-3,2,-1},{1,3,3,-2,-9},80] (* _Harvey P. Dale_, Aug 18 2016 *)
%K easy,sign
%O 0,2
%A _Paul Barry_, Oct 31 2004