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%I #4 Jul 25 2019 01:12:12
%S 1,0,-1,1,0,1,-2,1,0,1,-3,1,1,0,1,-4,-4,1,0,-1,8,9,-23,6,1,0,1,-13,
%T -41,106,-41,-13,1,0,1,-21,-146,484,-152,-186,19,1,0,1,-33,-492,1784,
%U 1784,-492,-33,1,0,-1,55,1359,-10701,-8552,27128,-7875,-1467,53,1,0,1,-89
%N Denominator coefficients of infinite over the Fibonacci sequence: p(x,n)=(1 - x)*Sum[Fibonacci[k]^n*x^k, {k, 0, Infinity}]; t(n,m)=Coefficients(Numerator(p(x,n)).
%C Row sums are:
%C {1, 0, 0, 0, -6, 0, 0, 0, 2520, 0, 0,...}.
%C The denominator and numerator polynomials appear to be new.
%F p(x,n)=(1 - x)*Sum[Fibonacci[k]^n*x^k, {k, 0, Infinity}]; t(n,m)=Coefficients(Numerator(p(x,n)).
%e {1},
%e {0, -1, 1},
%e {0, 1, -2, 1},
%e {0, 1, -3, 1, 1},
%e {0, 1, -4, -4, 1},
%e {0, -1, 8, 9, -23, 6, 1},
%e {0, 1, -13, -41, 106, -41, -13, 1},
%e {0, 1, -21, -146, 484, -152, -186, 19, 1},
%e {0, 1, -33, -492, 1784, 1784, -492, -33, 1},
%e {0, -1, 55, 1359, -10701, -8552, 27128, -7875, -1467, 53, 1},
%e {0, 1, -89, -3872, 50193, 117271, -327008, 117271, 50193, -3872, -89, 1}
%t Clear[t0, p, x, n, m];
%t p[x_, n_] = (1 - x)*Sum[Fibonacci[k]^n*x^k, {k, 0, Infinity}]
%t Table[Numerator[FullSimplify[ExpandAll[p[x, n]]]], {n, 0, 10}];
%t Table[CoefficientList[Numerator[FullSimplify[ExpandAll[p[x, n]]]], x], {n, 0, 10}];
%t Flatten[%]
%Y A000045
%K sign,tabl,uned
%O 0,7
%A _Roger L. Bagula_, Feb 04 2009
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