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Search: id:A122509
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| A122509 |
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Coefficient expansion of the root sum zero polynomial:p(x)=-21 - 2 x + x^3 as x/(1 - x^2(2 + 21 x)). |
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+0
1
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| 0, 1, 0, 2, 21, 4, 84, 449, 252, 2662, 9933, 10616, 75768, 229825, 374472, 2050778, 5575269, 11965468, 54216876, 141011585, 359708580, 1420577566, 3680660445, 10395035312, 37193449776, 98083939969, 292682641104, 977230325234
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OFFSET
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1,4
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COMMENT
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This sequence comes from investigating cubic root sum zero polynomials with rules: 1) p[x_] = Expand[Product[(x - a[n]), {n, 1, 3}]]=0 2) Sum[a[n], {n, 1, 3}]=0 Setting: a[1] = -a[2] - a[3] Solving for negative a[2] as first expansion term : Solve[a2^2 + a2 a3 + a3^2 == 2, a2] a[3]=3 Gives this sequence.
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FORMULA
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Coefficient expansion of x/(1 - x^2(2 + 21 x))
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MATHEMATICA
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p[x_]=-21 - 2 x + x^3 q[x_] = ExpandAll[x^3*p[1/x]] Table[ SeriesCoefficient[Series[x/q[x], {x, 0, 30}], n], {n, 0, 30}]
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CROSSREFS
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Sequence in context: A143247 A162536 A100980 this_sequence A024230 A105666 A058261
Adjacent sequences: A122506 A122507 A122508 this_sequence A122510 A122511 A122512
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KEYWORD
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nonn,uned
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AUTHOR
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Roger Bagula (rlbagulatftn(AT)yahoo.com), Sep 15 2006
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