This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A127630 #17 Nov 18 2020 15:37:30
%S A127630 1,1,-3,-3,5,5,-7,-7,9,9,-11,-11,13,13,-15,-15,17,17,-19,-19,21,21,
%T A127630 -23,-23,25,25,-27,-27,29,29,-31,-31,33,33,-35,-35,37,37,-39,-39,41,
%U A127630 41,-43,-43,45,45,-47,-47,49,49,-51,-51,53,53,-55,-55
%N A127630 Expansion of (1+x-x^2-x^3)/(1+x^2)^2.
%C A127630 Hankel transform of A045621(n+1).
%H A127630 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,-2,0,-1).
%F A127630 a(n) = (-1)^binomial(n,2) * ( 2*floor(n/2)+1 ).
%F A127630 a(n) = (n + 1 - (n mod 2))*(-1)^floor(n/2). [_Wesley Ivan Hurt_, Jun 30 2013]
%F A127630 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 A127630 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 A127630 Cf. A109613.
%K A127630 sign,easy
%O A127630 0,3
%A A127630 _Paul Barry_, Jan 20 2007