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Expansion of (1-x)^(-1)/(1+2*x-x^2-x^3).
1

%I #15 Jan 25 2020 00:40:58

%S 1,-1,4,-7,18,-38,88,-195,441,-988,2223,-4992,11220,-25208,56645,

%T -127277,285992,-642615,1443946,-3244514,7290360,-16381287,36808421,

%U -82707768,185842671,-417584688,938304280,-2108350576,4737420745,-10644887785,23918845740,-53745158519,120764274994

%N Expansion of (1-x)^(-1)/(1+2*x-x^2-x^3).

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (-1, 3, 0, -1).

%F a(n) = (-1)^n*A124400(n). - _Philippe Deléham_, Dec 18 2006

%F a(n) = a(n-1) + 3*a(n-2) - a(n-4); a(0)=1, a(1)=-1, a(2)=4, a(3)=-7. - _Harvey P. Dale_, Mar 13 2013

%t CoefficientList[Series[(1-x)^(-1)/(1+2x-x^2-x^3),{x,0,40}],x] (* or *) LinearRecurrence[{-1,3,0,-1},{1,-1,4,-7},40] (* _Harvey P. Dale_, Mar 13 2013 *)

%o (PARI) Vec((1-x)^(-1)/(1+2*x-x^2-x^3)+O(x^99)) \\ _Charles R Greathouse IV_, Sep 27 2012

%K sign,easy

%O 0,3

%A _N. J. A. Sloane_, Nov 17 2002