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A105291
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Triangle read by rows: T(m,n) = binomial(m!,n), m>=0, 0 <= n <= m!.
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3
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1, 1, 1, 1, 1, 2, 1, 1, 6, 15, 20, 15, 6, 1, 1, 24, 276, 2024, 10626, 42504, 134596, 346104, 735471, 1307504, 1961256, 2496144, 2704156, 2496144, 1961256, 1307504, 735471, 346104, 134596, 42504, 10626, 2024, 276, 24, 1, 1, 120, 7140, 280840, 8214570, 190578024
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OFFSET
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0,6
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COMMENTS
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This is the number of nXm arrays with each row a permutation of 1..m, and rows in lexicographically strictly increasing order.
For row 0, remember that 0!=1.
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LINKS
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EXAMPLE
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Triangle begins:
[1, 1],
[1, 1],
[1, 2, 1],
[1, 6, 15, 20, 15, 6, 1],
[1, 24, 276, 2024, 10626, 42504, 134596, 346104, 735471, 1307504, 1961256, 2496144, 2704156, 2496144, 1961256, 1307504, 735471, 346104, 134596, 42504, 10626, 2024, 276, 24, 1],
...
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MATHEMATICA
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Flatten[Table[Binomial[m!, n], {m, 0, 5}, {n, 0, m!}]] (* Harvey P. Dale, Apr 16 2013 *)
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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