%I A000315 M3690 N1508
%S A000315 1,1,1,4,56,9408,16942080,535281401856,377597570964258816,
%T A000315 7580721483160132811489280,5363937773277371298119673540771840
%N A000315 Number of reduced Latin squares of order n; labeled loops (quasigroups 
               with an identity element) and a fixed identity.
%D A000315 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000315 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000315 S. E. Bammel and J. Rothstein, The number of 9x9 Latin squares, Discrete 
               Math., 11 (1975), 93-95.
%D A000315 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 183.
%D A000315 R. A. Fisher and F. Yates, Statistical Tables for Biological, Agricultural 
               and Medical Research. 6th ed., Hafner, NY, 1963, p. 22.
%D A000315 B. D. McKay and I. M. Wanless, Latin squares of order eleven. Preprint 
               2004. http://cs.anu.edu.au/~bdm/papers/ls11.pdf
%D A000315 C. R. Rao, S. K. Mitra and A. Matthai, editors, Formulae and Tables for 
               Statistical Work. Statistical Publishing Society, Calcutta, India, 
               1966, p. 193.
%D A000315 J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 
               210.
%D A000315 H. J. Ryser, Combinatorial Mathematics. Mathematical Association of America, 
               Carus Mathematical Monograph 14, 1963, p. 53.
%D A000315 M. B. Wells, Elements of Combinatorial Computing. Pergamon, Oxford, 1971, 
               p. 240.
%D A000315 B. D. McKay and I. M. Wanless, On the number of Latin squares. Preprint 
               2004. http://cs.anu.edu.au/~bdm/papers/ls11.pdf
%H A000315 B. Cherowitzo, <a href="http://www-math.cudenver.edu/~wcherowi/courses/
               m6406/csln1.html#1">Comb. Structures Lecture Notes</a>
%H A000315 B. D. McKay and E. Rogoyski, <a href="http://www.combinatorics.org/Volume_2/
               volume2.html#N3">Latin squares of order ten</a>, Electron. J. Combinatorics, 
               2 (1995) #N3.
%H A000315 N. J. A. Sloane, <a href="http://www.research.att.com/~njas/doc/sg.txt">
               My favorite integer sequences</a>, in Sequences and their Applications 
               (Proceedings of SETA '98).
%H A000315 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               LatinSquare.html">Link to a section of The World of Mathematics.</
               a>
%H A000315 <a href="Sindx_La.html#Latin">Index entries for sequences related to 
               Latin squares and rectangles</a>
%H A000315 <a href="Sindx_Qua.html#quasigroups">Index entries for sequences related 
               to quasigroups</a>
%H A000315 B. D. McKay, A. Meynert, W. Myrvold, <a href="http://dx.doi.org/10.1002/
               jcd.20105">Small latin squares, quasigroups and loops</a>, J. Combin. 
               Designs, vol. 15, no. 2 (2007) pp 98-119.
%H A000315 B. D. McKay, I. M. Wanless, <a href="http://dx.doi.org/10.1007/s00026-005-0261-7">
               On the number of Latin squares</a>, Ann. Combinat. 9 (2005) 335-344.
%Y A000315 a(n) = A002860(n)/(n!*(n-1)!) = A000479(n)/(n-1)!. Cf. A003090, A040082, 
               A057771, A057997.
%Y A000315 Sequence in context: A000573 A070019 A056075 this_sequence A080984 A071579 
               A060497
%Y A000315 Adjacent sequences: A000312 A000313 A000314 this_sequence A000316 A000317 
               A000318
%K A000315 nonn,hard,nice,more
%O A000315 1,4
%A A000315 N. J. A. Sloane (njas(AT)research.att.com).
%E A000315 Added 6/95: the last (10th) term was probably first computed by Eric 
               Rogoyski
%E A000315 One more term (from the McKay-Wanless article) from Richard Bean (rwb(AT)eskimo.com), 
               Feb 17 2004