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 A158496 #16 Oct 05 2024 21:37:15
%S A158496 1,-4,-1,8,1,-12,-1,16,1,-20,-1,24,1,-28,-1,32,1,-36,-1,40,1,-44,-1,
%T A158496 48,1,-52,-1,56,1,-60,-1,64,1,-68,-1,72,1,-76,-1,80,1,-84,-1,88,1,-92,
%U A158496 -1,96,1,-100,-1,104,1,-108,-1,112,1,-116,-1,120,1,-124,-1,128,1,-132,-1
%N A158496 Expansion of (1-4x+x^2)/(1+x^2)^2.
%C A158496 Hankel transform of A158495.
%H A158496 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,-2,0,-1).
%F A158496 a(n) = (n+3/2-(n+1/2)*(-1)^n)*(-1)^C(n+1,2).
%F A158496 a(0)=1, a(1)=-4, a(2)=-1, a(3)=8, a(n) = -2*a(n-2)-a(n-4). - _Harvey P. Dale_, Mar 06 2012
%t A158496 CoefficientList[Series[(1-4x+x^2)/(1+x^2)^2,{x,0,70}],x] (* or *) LinearRecurrence[{0,-2,0,-1},{1,-4,-1,8},70] (* _Harvey P. Dale_, Mar 06 2012 *)
%o A158496 (PARI) Vec((1-4*x+x^2)/(1+x^2)^2 + O(x^100)) \\ _Altug Alkan_, Jan 10 2016
%Y A158496 Cf. A019425.
%K A158496 easy,sign
%O A158496 0,2
%A A158496 _Paul Barry_, Mar 20 2009