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Search: id:A143083
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| A143083 |
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A triangle of coefficients: t(n,m)=(2*n + 2*m + 3)!/(28(2*m + 1)!(2*n + 1)!). |
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+0
1
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| 3, 10, 70, 21, 252, 1386, 36, 660, 5148, 25740, 55, 1430, 15015, 97240, 461890, 78, 2730, 37128, 302328, 1763580, 8112468, 105, 4760, 81396, 813960, 5720330, 31201800, 140408100, 136, 7752, 162792, 1961256, 16343800, 104303160
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Row sums are:
{3, 80, 1659, 31584, 575630, 10218312, 178230451, 3070011776, 52387009722, 887453729920, 14946680628638};
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REFERENCES
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Maryam Mirzakhani,Weil-Peteresson volumes and intersection theory on the moduli space of curves, Journal of the American Mathematical Society,page 18, http://www.math.princeton.edu/~mmirzakh/
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FORMULA
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t(n,m)=(2*n + 2*m + 3)!/(28(2*m + 1)!(2*n + 1)!).
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EXAMPLE
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{3},
{10, 70},
{21, 252, 1386},
{36, 660, 5148, 25740},
{55, 1430, 15015, 97240, 461890},
{78, 2730, 37128, 302328, 1763580, 8112468},
{105, 4760, 81396, 813960, 5720330, 31201800, 140408100},
{136, 7752, 162792, 1961256, 16343800, 104303160, 542911320, 2404321560},
{171, 11970, 302841, 4326300, 42181425, 311375610, 1856277675, 9334424880, 40838108850},
{210, 17710, 531300, 8880300, 100150050, 846723150, 5731664400, 32479431600, 159053687100, 689232644100},
{253, 25300, 888030, 17168580, 221760825, 2128903920, 16239715800, 103006197360, 561232295910, 2691289372200, 11572544300460}
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MATHEMATICA
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t[n_, m_] = (2*n + 2*m + 3)!/((2*m + 1)!(2*n + 1)!); Table[Table[t[n, m]/2, {m, 0, n}], {n, 0, 10}]; Flatten[%]
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CROSSREFS
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Sequence in context: A004102 A072638 A080526 this_sequence A002499 A047833 A047834
Adjacent sequences: A143080 A143081 A143082 this_sequence A143084 A143085 A143086
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KEYWORD
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nonn,uned
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AUTHOR
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Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Oct 15 2008
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