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Expansion of (1+5x-40x^2)/((1-5x)(1+5x)).
0

%I #8 Dec 26 2015 11:55:34

%S 1,5,-15,125,-375,3125,-9375,78125,-234375,1953125,-5859375,48828125,

%T -146484375,1220703125,-3662109375,30517578125,-91552734375,

%U 762939453125,-2288818359375,19073486328125,-57220458984375,476837158203125,-1430511474609375

%N Expansion of (1+5x-40x^2)/((1-5x)(1+5x)).

%C a(0)=1, a(2n-1)=k^(2n-1), a(2n)=(2-k)k^(2n-1), k=5; G.f.: (1+kx+(2-2k)kx^2)/((1-kx)(1+kx)), k=5.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,25).

%F a(n)=5^n/5 +(-4)(-5)^n/5+8*0^n/5

%t CoefficientList[Series[(1+5x-40x^2)/((1-5x)(1+5x)),{x,0,30}],x] (* or *) LinearRecurrence[{0,25},{1,5,-15},30] (* _Harvey P. Dale_, Dec 26 2015 *)

%K easy,sign

%O 0,2

%A _Paul Barry_, Dec 19 2003