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A158613
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A sequence of quadratic coefficients from an infinite sum polynomial: p(x,n)=n*x/(Sum[n^k*Fibonacci[k]*x^k, {k, 0, Infinity}]).
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0
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1, 1, -1, -1, 1, -2, -4, 1, -3, -9, 1, -4, -16, 1, -5, -25, 1, -6, -36, 1, -7, -49, 1, -8, -64, 1, -9, -81, 1, -10, -100
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,6
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COMMENTS
| Quadratic sums are:
{1, -1, -5, -11, -19, -29, -41, -55, -71, -89, -109,...}.
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FORMULA
| p(x,n)=n*x/(Sum[n^k*Fibonacci[k]*x^k, {k, 0, Infinity}]); t(n,m)=coefficients(p(x,n),x)
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EXAMPLE
| {1},
{1, -1, -1},
{1, -2, -4},
{1, -3, -9},
{1, -4, -16},
{1, -5, -25},
{1, -6, -36},
{1, -7, -49},
{1, -8, -64},
{1, -9, -81},
{1, -10, -100}
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MATHEMATICA
| Clear[t0, p, x, n, m];
p[x_, n_] = FullSimplify[n*x/(Sum[n^k*Fibonacci[k]*x^k, {k, 0, Infinity}])];
Table[ExpandAll[p[x, n]], {n, 0, 10}];
Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}];
Flatten[%]
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CROSSREFS
| A156133
Sequence in context: A011233 A163360 A076053 * A100075 A059836 A069270
Adjacent sequences: A158610 A158611 A158612 * A158614 A158615 A158616
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KEYWORD
| sign,tabl,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 22 2009
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