|
| |
|
|
A008300
|
|
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.
|
|
1
| |
|
|
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; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,5
|
|
|
COMMENTS
| 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.
|
|
|
REFERENCES
| 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.
|
|
|
FORMULA
| 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.
|
|
|
EXAMPLE
| 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,
|
|
|
CROSSREFS
| Diagonals give A000142, A001499, A001501, A058527.
Sequence in context: A174411 A155795 A009963 * A173887 A137376 A039761
Adjacent sequences: A008297 A008298 A008299 * A008301 A008302 A008303
|
|
|
KEYWORD
| tabl,nonn,nice
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| More terms from Greg Kuperberg (greg(AT)math.ucdavis.edu), Feb 08 2001
|
| |
|
|
