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%I #14 Aug 25 2023 15:14:28
%S 1,-2,1,0,-1,2,-3,4,-5,6,-7,8,-9,10,-11,12,-13,14,-15,16,-17,18,-19,
%T 20,-21,22,-23,24,-25,26,-27,28,-29,30,-31,32,-33,34,-35,36,-37,38,
%U -39,40,-41,42,-43,44,-45,46,-47,48,-49,50,-51,52,-53,54,-55,56,-57
%N Expansion of (1 - 2*x^2)/(1 + x)^2. First column of Riordan triangle A248156.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (-2,-1).
%F O.g.f.: (1 - 2*x^2)/(1 + x)^2 = -2 + 4/(1+x) - 1/(1+x)^2.
%F a(n) = -2*delta(n,0) + (-1)^n*(3 - n), n >= 0, with Kronecker delta(n,0) = 1 if n=0 else 0.
%F a(0) = 1, a(n) = -2*a(n-1) - a(n-2), n >= 3, with a(1) = -2, a(2) = 1.
%F a(n) = A038608(n-3) = A097141(n-1), n>=3.
%t CoefficientList[Series[(1-2x^2)/(1+x)^2,{x,0,60}],x] (* or *) LinearRecurrence[{-2,-1},{1,-2,1},60] (* _Harvey P. Dale_, Aug 25 2023 *)
%o (PARI) Vec((1 - 2*x^2)/(1 + x)^2 + O(x^80)) \\ _Michel Marcus_, Oct 11 2014
%Y Cf. A248156 (row k=0).
%K sign,easy,less
%O 0,2
%A _Wolfdieter Lang_, Oct 05 2014