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A000479
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Number of 1-factorizations of K_{n,n}.
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6
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1, 1, 1, 2, 24, 1344, 1128960, 12198297600, 2697818265354240, 15224734061278915461120, 2750892211809148994633229926400, 19464657391668924966616671344752852992000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Also, number of latin squares of order n with first row 1,2,...,n.
Also number of fixed diagonal Latin squares of order n. - Eric Weisstein (eric(AT)weisstein.com), Dec 18, 2005
Also maximum number of Latin squares of order n such that no two of them have all the same rows (respectively, columns). - Rick L. Shepherd (rshepherd2(AT)hotmail.com), Mar 01 2008
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REFERENCES
| CRC Handbook of Combinatorial Designs, 1996, p. 660.
Denes and Keedwell, Latin Squares and Applications, Academic Press 1974.
B. D. McKay and I. M. Wanless, On the number of Latin squares. Preprint 2004. http://cs.anu.edu.au/~bdm/papers/ls11.pdf
D. S. Stones, The many formulae for the number of Latin rectangles, Electron. J. Combin 17 (2010), A1.
D. S. Stones and I. M. Wanless, Divisors of the number of Latin rectangles, J. Combin. Theory Ser. A 117 (2010), 204-215.
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LINKS
| B. D. McKay, A. Meynert and W. Myrvold, Small Latin Squares, Quasigroups and Loops, J. Combin. Designs, to appear (2005).
B. D. McKay and I. M. Wanless, On the number of Latin squares, Ann. Combinat. 9 (2005) 335-344.
Eric Weisstein's World of Mathematics, Latin Square
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CROSSREFS
| a(n) = A000315(n)*(n-1)! = A002860(n)/n!. Cf. A000528.
Sequence in context: A137887 A028365 A094050 * A181231 A111427 A081955
Adjacent sequences: A000476 A000477 A000478 * A000480 A000481 A000482
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KEYWORD
| nonn,hard,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| One more term (from the McKay-Wanless article) from Richard Bean (rwb(AT)eskimo.com), Feb 17 2004
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