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 A156135 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(Numberator(p(x,n)). 0
 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, -41, 106, -41, -13, 1, 0, 1, -21, -146, 484, -152, -186, 19, 1, 0, 1, -33, -492, 1784, 1784, -492, -33, 1, 0, -1, 55, 1359, -10701, -8552, 27128, -7875, -1467, 53, 1, 0, 1, -89 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 COMMENTS Row sums are: {1, 0, 0, 0, -6, 0, 0, 0, 2520, 0, 0,...}. The denominator and numerator polynomials appear to be new. LINKS FORMULA p(x,n)=(1 - x)*Sum[Fibonacci[k]^n*x^k, {k, 0, Infinity}]; t(n,m)=Coefficients(Numerator(p(x,n)). EXAMPLE {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, -41, 106, -41, -13, 1}, {0, 1, -21, -146, 484, -152, -186, 19, 1}, {0, 1, -33, -492, 1784, 1784, -492, -33, 1}, {0, -1, 55, 1359, -10701, -8552, 27128, -7875, -1467, 53, 1}, {0, 1, -89, -3872, 50193, 117271, -327008, 117271, 50193, -3872, -89, 1} MATHEMATICA Clear[t0, p, x, n, m]; p[x_, n_] = (1 - x)*Sum[Fibonacci[k]^n*x^k, {k, 0, Infinity}] Table[Numerator[FullSimplify[ExpandAll[p[x, n]]]], {n, 0, 10}]; Table[CoefficientList[Numerator[FullSimplify[ExpandAll[p[x, n]]]], x], {n, 0, 10}]; Flatten[%] CROSSREFS Sequence in context: A030528 A077227 A089263 * A047265 A185962 A279928 Adjacent sequences:  A156132 A156133 A156134 * A156136 A156137 A156138 KEYWORD sign,tabl,uned AUTHOR Roger L. Bagula, Feb 04 2009 STATUS approved

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Last modified October 17 05:23 EDT 2018. Contains 316275 sequences. (Running on oeis4.)