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A231148 Array of coefficients of numerator polynomials of the rational function p(n, x - 1/x), where p(n,x) = (x^n - 1)/(x - 1). 1

%I #4 Nov 07 2013 03:33:00

%S 1,-1,1,1,1,-1,-1,1,1,-1,1,2,-1,-2,1,1,1,-1,-3,2,5,-2,-3,1,1,-1,1,4,

%T -3,-8,5,8,-3,-4,1,1,1,-1,-5,4,12,-8,-15,8,12,-4,-5,1,1,-1,1,6,-5,-17,

%U 12,27,-15,-27,12,17,-5,-6,1,1,1,-1,-7,6,23,-17,-44

%N Array of coefficients of numerator polynomials of the rational function p(n, x - 1/x), where p(n,x) = (x^n - 1)/(x - 1).

%e First 4 rows:

%e 1

%e -1 1 1

%e 1 -1 -1 1 1

%e -1 1 2 -1 -2 1 1

%e First 4 polynomials: 1, -1 + x + x^2, 1 - x - x^2 + x^3 + x^4

%t z = 60; p[n_, x_] := p[x] = (x^n - 1)/(x - 1); Table[p[n, x], {n, 1, z/4}]; f1[n_, x_] := f1[n, x] = Numerator[Factor[p[n, x] /. x -> x - 1/x]]; Table[Expand[f1[n, x]], {n, 0, z/4}]

%t Flatten[Table[CoefficientList[f1[n, x], x], {n, 1, z/4}]]

%Y Cf. A231147.

%K tabf,sign,easy

%O 1,12

%A _Clark Kimberling_, Nov 05 2013

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Last modified March 28 13:35 EDT 2024. Contains 371254 sequences. (Running on oeis4.)