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A137267
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Chung-Graham juggling polynomials as a triangular sequence of positive coefficients.
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0
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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; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| Row sums are 1, 2, 6, 16, 50, 204, 1078, 6992, 53226, 462340,.., might be A014144(n)-1 for n>=2.
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LINKS
| Fan Chung, Ron Graham, Primitive juggling sequences, Am. Math. Monthly 115 (3) (2008) 185-194
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FORMULA
| 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
| 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
| 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
| Cf. A137948.
Sequence in context: A074732 A089046 A054911 * A123576 A094824 A029054
Adjacent sequences: A137264 A137265 A137266 * A137268 A137269 A137270
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KEYWORD
| nonn,tabl,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 12 2008
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