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Search: id:A008300
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| A008300 |
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Triangle read by rows: T(n,k) (n >= 0, 0<=k<=n) gives number of {0,1} n X n matrices with all row and column sums equal to k. |
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+0
2
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| 1, 1, 1, 1, 2, 1, 1, 6, 6, 1, 1, 24, 90, 24, 1, 1, 120, 2040, 2040, 120, 1, 1, 720, 67950, 297200, 67950, 720, 1, 1, 5040, 3110940, 68938800, 68938800, 3110940, 5040, 1, 1, 40320, 187530840, 24046189440, 116963796250, 24046189440, 187530840, 40320, 1, 1, 362880, 14398171200, 12025780892160, 315031400802720, 315031400802720, 12025780892160, 14398171200, 362880, 1
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Or, triangle of multipermutation numbers T(n,k), n >= 0, 0<=k<=n: number of relations on an n-set such that all vertical sections and all horizontal sections have k elements.
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REFERENCES
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L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 236, P(n,k).
C. J. Everett and P. R. Stein, The asymptotic number of integer stochastic matrices, Disc. Math. 1 (1971), 55-72.
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FORMULA
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Comtet quotes Everett and Stein as showing that T(n,k) ~ (kn)!(k!)^(-2n) exp( -(k-1)^2/2 ) for fixed k as n -> oo.
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EXAMPLE
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Triangle begins:
1,
1,1,
1,2,1,
1,6,6,1,
1,24,90,24,1,
1,120,2040,2040,120,1,
1,720,67950,297200,67950,720,1,
1,5040,3110940,68938800,68938800,3110940,5040,1,
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CROSSREFS
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Diagonals give A000142, A001499, A001501, A058527.
Sequence in context: A145903 A155795 A009963 this_sequence A137376 A039761 A144089
Adjacent sequences: A008297 A008298 A008299 this_sequence A008301 A008302 A008303
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KEYWORD
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tabl,nonn,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Greg Kuperberg (greg(AT)math.ucdavis.edu), Feb 08 2001
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