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A156133 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(Denominator(p(x,n)). 1
1, -1, 1, 1, 1, -2, -2, 1, 1, -3, -6, 3, 1, 1, -4, -19, -4, 1, -1, 8, 40, -60, -40, 8, 1, 1, -13, -104, 260, 260, -104, -13, 1, 1, -21, -273, 1092, 1820, -1092, -273, 21, 1, 1, -33, -747, 3894, 16270, 3894, -747, -33, 1, -1, 55, 1870, -19635, -85085, 136136, 85085 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

Row sums are:

{1, 1, -2, -4, -25, -44, 288, 1276, 22500, 96976, -1707552,...}.

The denominator and numerator polynomials appear to be new.

LINKS

Table of n, a(n) for n=0..57.

FORMULA

p(x,n)=(1 - x)*Sum[Fibonacci[k]^n*x^k, {k, 0, Infinity}]; t(n,m)=Coefficients(Denominator(p(x,n)).

EXAMPLE

{1},

{-1, 1, 1},

{1, -2, -2, 1},

{1, -3, -6, 3, 1},

{1, -4, -19, -4, 1},

{-1, 8, 40, -60, -40, 8, 1},

{1, -13, -104, 260, 260, -104, -13, 1},

{1, -21, -273, 1092, 1820, -1092, -273, 21, 1},

{1, -33, -747, 3894, 16270, 3894, -747, -33, 1},

{-1, 55, 1870, -19635, -85085, 136136, 85085, -19635, -1870, 55, 1},

{1, -89, -4895, 83215, 582505, -1514513, -1514513, 582505, 83215, -4895, -89, 1}

MATHEMATICA

Clear[t0, p, x, n, m];

p[x_, n_] = (1 - x)*Sum[Fibonacci[k]^n*x^k, {k, 0, Infinity}]

Table[Denominator[FullSimplify[ExpandAll[p[x, n]]]], {n, 0, 10}];

Flatten[%]

CROSSREFS

A000045, A055870

Sequence in context: A131791 A010358 A155865 * A010048 A055870 A088459

Adjacent sequences:  A156130 A156131 A156132 * A156134 A156135 A156136

KEYWORD

sign,tabl,uned

AUTHOR

Roger L. Bagula, Feb 04 2009

STATUS

approved

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Last modified February 19 16:02 EST 2019. Contains 320311 sequences. (Running on oeis4.)