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A140805
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Triangle T(n, k) read by rows T(n,k) = binomial(n, k)^binomial(n, k).
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0
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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
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OFFSET
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1,5
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COMMENTS
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Sequence of coefficients inspired by the Belyi transform: x'->(m + n)^(n + m)*x^m*(1 - x)^n/(m^m*n^n).
Row sums are: 1, 2, 6, 56, 47170, 20000006252, 104857600875787780761812064, ...
These symmetrical coefficients remind one of Calabi-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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LINKS
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FORMULA
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T(n,k) = binomial(n, k)^binomial(n, k).
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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},
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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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KEYWORD
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AUTHOR
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STATUS
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approved
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