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Search: id:A137267
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| A137267 |
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Chung-Graham juggling polynomials as a triangular sequence of positive coefficients. |
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1
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| 1, 1, 1, 2, 2, 2, 3, 3, 4, 6, 4, 4, 6, 12, 24, 5, 5, 8, 18, 48, 120, 6, 6, 10, 24, 72, 240, 720, 7, 7, 12, 30, 96, 360, 1440, 5040, 8, 8, 14, 36, 120, 480, 2160, 10080, 40320, 9, 9, 16, 42, 144, 600, 2880, 15120, 80640, 362880
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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Row sums sequence is:
{1, 2, 6, 16, 50, 204, 1078, 6992, 53226, 462340}
A set of matrices can be associated with these polynomials.
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REFERENCES
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http://www.maa.org/pubs/monthly_mar08_toc.html; Primitive Juggling Sequences; By: Fan Chung and Ron Graham; fan(AT)ucsd.edu, graham(AT)ucsd.edu; page 190
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FORMULA
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f_b(x)=(1 - Sum[(n - k)*k!*x^k, {k, 0, n - 1}])/(1-(b+1)*x) p(x,b)=-f_b(x)*(1-(b+1)*x)=-(1 - Sum[(n - k)*k!*x^k, {k, 0, n - 1}])
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EXAMPLE
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{1},
{1, 1},
{2, 2, 2},
{3, 3, 4, 6},
{4, 4, 6, 12, 24},
{5, 5, 8, 18, 48, 120},
{6, 6, 10, 24, 72, 240, 720},
{7, 7, 12, 30, 96, 360, 1440, 5040},
{8, 8, 14, 36, 120, 480, 2160, 10080, 40320},
{9, 9, 16, 42, 144, 600, 2880, 15120, 80640, 362880}
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MATHEMATICA
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p[x_, n_] := If[n == 1, 1, -(1 - Sum[(n - k)*k!*x^k, {k, 0, n - 1}])]; a = Table[CoefficientList[p[x, n], x], {n, 1, 10}]; Flatten[a]
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CROSSREFS
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Sequence in context: A074732 A089046 A054911 this_sequence A123576 A094824 A029054
Adjacent sequences: A137264 A137265 A137266 this_sequence A137268 A137269 A137270
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KEYWORD
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nonn,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 12 2008
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