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%I #13 Jan 11 2016 03:21:21
%S 1,-4,-1,8,1,-12,-1,16,1,-20,-1,24,1,-28,-1,32,1,-36,-1,40,1,-44,-1,
%T 48,1,-52,-1,56,1,-60,-1,64,1,-68,-1,72,1,-76,-1,80,1,-84,-1,88,1,-92,
%U -1,96,1,-100,-1,104,1,-108,-1,112,1,-116,-1,120,1,-124,-1,128,1,-132,-1
%N Expansion of (1-4x+x^2)/(1+x^2)^2.
%C Hankel transform of A158495.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0, -2, 0, -1).
%F a(n) = ((n+3/2-(n+1/2)*(-1)^n)*(-1)^C(n+1,2).
%F 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 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 (PARI) Vec((1-4*x+x^2)/(1+x^2)^2 + O(x^100)) \\ _Altug Alkan_, Jan 10 2016
%Y Cf. A019425.
%K easy,sign
%O 0,2
%A _Paul Barry_, Mar 20 2009
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