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Search: id:A000479
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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; listen)
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OFFSET
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0,4
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COMMENT
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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
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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
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LINKS
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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
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a(n) = A000315(n)*(n-1)! = A002860(n)/n!. Cf. A000528.
Adjacent sequences: A000476 A000477 A000478 this_sequence A000480 A000481 A000482
Sequence in context: A137887 A094050 A028365 this_sequence A111427 A081955 A163086
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KEYWORD
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nonn,hard,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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One more term (from the McKay-Wanless article) from Richard Bean (rwb(AT)eskimo.com), Feb 17 2004
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