%I #17 Nov 18 2020 15:37:30
%S 1,1,-3,-3,5,5,-7,-7,9,9,-11,-11,13,13,-15,-15,17,17,-19,-19,21,21,
%T -23,-23,25,25,-27,-27,29,29,-31,-31,33,33,-35,-35,37,37,-39,-39,41,
%U 41,-43,-43,45,45,-47,-47,49,49,-51,-51,53,53,-55,-55
%N Expansion of (1+x-x^2-x^3)/(1+x^2)^2.
%C Hankel transform of A045621(n+1).
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,-2,0,-1).
%F a(n) = (-1)^binomial(n,2) * ( 2*floor(n/2)+1 ).
%F a(n) = (n + 1 - (n mod 2))*(-1)^floor(n/2). [_Wesley Ivan Hurt_, Jun 30 2013]
%F G.f.: 1/(G(0) - x), where G(k) = x*(2*k+1) - (2*k-1)/( 1 + x/( 1 - x*(2*k+3)/G(k+1) )); (continued fraction ). - _Sergei N. Gladkovskii_, Dec 27 2013
%t CoefficientList[Series[(1+x-x^2-x^3)/(1+x^2)^2,{x,0,100}],x] (* or *) LinearRecurrence[{0,-2,0,-1},{1,1,-3,-3},100] (* _Harvey P. Dale_, Nov 18 2020 *)
%Y Cf. A109613.
%K sign,easy
%O 0,3
%A _Paul Barry_, Jan 20 2007