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Search: id:A144484
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| A144484 |
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A triangle sequence from a polynomial: p(x,n)=Sum[Binomial[3*n + 1 - m, n - m]*x^m, {m, 0, n}]; p(x,n)=Gamma[2*n+3]*Hypergeometric2F1[1,-n-1-3*n,x]/(Gamma[1+n]*Gamma[2+2*n}). |
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1
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| 1, 4, 1, 21, 6, 1, 120, 36, 8, 1, 715, 220, 55, 10, 1, 4368, 1365, 364, 78, 12, 1, 27132, 8568, 2380, 560, 105, 14, 1, 170544, 54264, 15504, 3876, 816, 136, 16, 1, 1081575, 346104, 100947, 26334, 5985, 1140, 171, 18, 1, 6906900, 2220075, 657800, 177100
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Row sums are:{1, 5, 28, 165, 1001, 6188, 38760, 245157, 1562275, 10015005, 64512240}.
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REFERENCES
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http://arxiv.org/abs/0704.3398v2; Almost Product Evaluation of Hankel Determinants Authors: Omer Egecioglu, Timothy Redmond, Charles Ryavec; http://tigraworld.com/diffdetnb/; http://tigraworld.com/diffdetnb/raw/matrix36.nb
M. Jones, Further remarks on the enumeration of graphs, preprint, 2001.
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FORMULA
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p(x,n)=Sum[Binomial[3*n + 1 - m, n - m]*x^m, {m, 0, n}]; p(x,n)=Gamma[2*n+3]*Hypergeometric2F1[1,-n-1-3*n,x]/(Gamma[1+n]*Gamma[2+2*n});
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EXAMPLE
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{1},
{4, 1},
{21, 6, 1},
{120, 36, 8, 1},
{715, 220, 55, 10, 1},
{4368, 1365, 364, 78, 12, 1},
{27132, 8568, 2380, 560, 105, 14, 1},
{170544, 54264, 15504, 3876, 816, 136, 16, 1},
{1081575, 346104, 100947, 26334, 5985, 1140, 171, 18, 1},
{6906900, 2220075, 657800, 177100, 42504, 8855, 1540, 210, 20, 1},
{44352165, 14307150, 4292145, 1184040, 296010, 65780, 12650, 2024, 253, 22, 1}
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MATHEMATICA
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p[x_, n_] = Sum[Binomial[3*n + 1 - m, n - m]*x^m, {m, 0, n}]; Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[%]
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CROSSREFS
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Sequence in context: A143497 A144354 A049352 this_sequence A121336 A126457 A159841
Adjacent sequences: A144481 A144482 A144483 this_sequence A144485 A144486 A144487
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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), Oct 12 2008
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