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A342890
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Triangle read by rows: T(n,k) = generalized binomial coefficients (n,k)_11 (n >= 0, 0 <= k <= n).
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13
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1, 1, 1, 1, 12, 1, 1, 78, 78, 1, 1, 364, 2366, 364, 1, 1, 1365, 41405, 41405, 1365, 1, 1, 4368, 496860, 2318680, 496860, 4368, 1, 1, 12376, 4504864, 78835120, 78835120, 4504864, 12376, 1, 1, 31824, 32821152, 1837984512, 6892441920, 1837984512, 32821152, 31824, 1
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OFFSET
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0,5
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COMMENTS
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For references, links, programs, etc., see earlier sequences in this series, especially A342889.
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LINKS
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FORMULA
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The generalized binomial coefficient (n,k)_m = Product_{j=1..k} binomial(n+m-j,m)/binomial(j+m-1,m).
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EXAMPLE
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Triangle begins:
[1],
[1, 1],
[1, 12, 1],
[1, 78, 78, 1],
[1, 364, 2366, 364, 1],
[1, 1365, 41405, 41405, 1365, 1],
[1, 4368, 496860, 2318680, 496860, 4368, 1],
[1, 12376, 4504864, 78835120, 78835120, 4504864, 12376, 1],
[1, 31824, 32821152, 1837984512, 6892441920, 1837984512, 32821152, 31824, 1],
...
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PROG
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(PARI) f(n, k, m) = prod(j=1, k, binomial(n-j+m, m)/binomial(j-1+m, m));
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CROSSREFS
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Triangles of generalized binomial coefficients (n,k)_m (or generalized Pascal triangles) for m = 1,...,12: A007318 (Pascal), A001263, A056939, A056940, A056941, A142465, A142467, A142468, A174109, A342889, A342890, A342891.
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KEYWORD
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AUTHOR
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STATUS
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approved
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