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Search: id:A140805
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| A140805 |
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Positive triangular sequence of coefficients inspired by the Belyi transform: x'->(m + n)^(n + m)*x^m*(1 - x)^n/(m^m*n^n): t(n,m)=Binomial[n, m]^Binomial[n, m]. |
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+0
1
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| 1, 1, 1, 1, 4, 1, 1, 27, 27, 1, 1, 256, 46656, 256, 1, 1, 3125, 10000000000, 10000000000, 3125, 1, 1, 46656, 437893890380859375, 104857600000000000000000000, 437893890380859375, 46656, 1, 1, 823543, 5842587018385982521381124421
(list; table; graph; listen)
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OFFSET
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1,5
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COMMENT
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Row sums are: 1, 2, 6, 56, 47170, 20000006252, 104857600875787780761812064, ...
These symmetrical coefficients remind one of Calbi-Yau base Hodge Diamond matrices. These numbers get large very fast.
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REFERENCES
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Leila Schneps (editor), The Grothendieck Theory of Dessins D'enfants, London Mathematical Society, Cambridge Press, page 49
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FORMULA
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t(n,m)=Binomial[n, m]^Binomial[n, m].
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EXAMPLE
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{1},
{1, 1},
{1, 4, 1},
{1, 27, 27, 1},
{1, 256, 46656, 256, 1},
{1, 3125, 10000000000, 10000000000, 3125, 1},
{1, 46656, 437893890380859375, 104857600000000000000000000, 437893890380859375, 46656, 1},
{1, 823543, 5842587018385982521381124421, 1102507499354148695951786433413508348166942596435546875, 1102507499354148695951786433413508348166942596435546875, 5842587018385982521381124421, 823543, 1}
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MATHEMATICA
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Clear[t, n, m, a] t[n_, m_] = Binomial[n, m]^Binomial[n, m]; a = Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[a]
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CROSSREFS
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Sequence in context: A113716 A088158 A136449 this_sequence A113370 A078536 A158390
Adjacent sequences: A140802 A140803 A140804 this_sequence A140806 A140807 A140808
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KEYWORD
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nonn,tabl
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AUTHOR
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Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Jul 15 2008
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