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%I #12 Oct 23 2019 07:10:27
%S 1,-1,-1,-1,2,1,1,-3,-1,-1,4,1,1,-5,-1,-1,6,1,1,-7,-1,-1,8,1,1,-9,-1,
%T -1,10,1,1,-11,-1,-1,12,1,1,-13,-1,-1,14,1,1,-15,-1,-1,16,1,1,-17,-1,
%U -1,18,1,1,-19,-1,-1,20,1,1
%N Expansion of (1 - x - x^2 + x^3 - x^5) / ((1 + x)^2*(1 - x + x^2)^2).
%C Hankel transform of A157127.
%H Colin Barker, <a href="/A157128/b157128.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,-2,0,0,-1).
%F a(n) = -2*a(n-3) - a(n-6) for n>5. - _Colin Barker_, Oct 23 2019
%t CoefficientList[Series[(1-x-x^2+x^3-x^5)/(1+2x^3+x^6),{x,0,60}],x] (* or *) LinearRecurrence[{0,0,-2,0,0,-1},{1,-1,-1,-1,2,1},70] (* _Harvey P. Dale_, Jul 08 2019 *)
%o (PARI) Vec((1 - x - x^2 + x^3 - x^5) / ((1 + x)^2*(1 - x + x^2)^2) + O(x^80)) \\ _Colin Barker_, Oct 23 2019
%K easy,sign
%O 0,5
%A _Paul Barry_, Feb 23 2009