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A002860 Number of Latin squares of order n; or labeled quasigroups.
(Formerly M2051 N0812)
+0
19
1, 2, 12, 576, 161280, 812851200, 61479419904000, 108776032459082956800, 5524751496156892842531225600, 9982437658213039871725064756920320000, 776966836171770144107444346734230682311065600000 (list; graph; listen)
OFFSET

1,2

REFERENCES

S. E. Bammel and J. Rothstein, The number of 9x9 Latin squares, Discrete Math., 11 (1975), 93-95.

J. W. Brown, Enumeration of Latin squares with application to order 8, J. Combin. Theory, 5 (1968), 177-184.

J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 210.

H. J. Ryser, Combinatorial Mathematics. Mathematical Association of America, Carus Mathematical Monograph 14, 1963, p. 53.

M. B. Wells, The number of Latin squares of order 8, J. Combin. Theory, 3 (1967), 98-99.

B. D. McKay and I. M. Wanless, On the number of Latin squares. Preprint 2004. http://cs.anu.edu.au/~bdm/papers/ls11.pdf

LINKS

B. D. McKay and E. Rogoyski, Latin squares of order ten, Electron. J. Combinatorics, 2 (1995) #N3.

T. Sillke, How many Latin Squares of order-N are there?

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Index entries for sequences related to Latin squares and rectangles

Index entries for sequences related to quasigroups

B. D. McKay, I. M. Wanless, On the number of Latin squares, Ann. Combinat. 9 (2005) 335-344.

CROSSREFS

Equals n!*A000479(n) = n!*(n-1)!*A000315(n). Cf. A003090, A040082, A057991.

Adjacent sequences: A002857 A002858 A002859 this_sequence A002861 A002862 A002863

Sequence in context: A013173 A013147 A050643 this_sequence A108078 A052129 A060055

KEYWORD

hard,nonn,nice

AUTHOR

njas

EXTENSIONS

One more term (from the McKay-Wanless article) from Richard Bean (rwb(AT)eskimo.com), Feb 17 2004

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Last modified October 7 14:39 EDT 2008. Contains 144666 sequences.


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