%I #38 Jun 28 2023 16:01:51
%S 1,1,1,6,396,526915620,1132835421602062347
%N Number of nonisomorphic 1-factorizations of complete graph K_{2n}.
%C Number of essentially different ways of scheduling a tournament of 2n teams.
%D CRC Handbook of Combinatorial Designs (see pages 655, 720-723).
%D Jeffrey H. Dinitz, David K. Garnick, Brendan D. McKay, There are 526,915,620 nonisomorphic one-factorizations of K_{12}. J. Combin. Des. 2 (1994), no. 4, 273-285.
%D Petteri Kaski and Patric R. J. Östergård, There are 1,132,835,421,602,062,347 nonisomorphic one-factorizations of K_{14}, Journal of Combinatorial Designs 17 (2009), pp. 147-159.
%D Charles C. Lindner, Eric Mendelsohn, and Alexander Rosa. "On the number of 1-factorizations of the complete graph." Journal of Combinatorial Theory, Series B 20.3 (1976): 265-282.
%D E. Seah and D. R. Stinson, On the enumeration of one-factorizations of complete graphs containing prescribed automorphism groups. Math. Comp. 50 (1988), 607-618.
%D W. D. Wallis, 1-Factorizations of complete graphs, pp. 593-631 in Jeffrey H. Dinitz and D. R. Stinson, Contemporary Design Theory, Wiley, 1992.
%H Petteri Kaski and Patric R. J. Östergård, <a href="http://arxiv.org/abs/0801.0202">There are 1,132,835,421,602,062,347 nonisomorphic one-factorizations of K_{14}</a>, arXiv:0801.0202 [math.CO], 2007.
%H Joseph Malkevitch, <a href="http://www1.ams.org/samplings/feature-column/fcarc-sports">Mathematics and Sports</a>
%H Brendan D. McKay and Ian M. Wanless, <a href="https://arxiv.org/abs/2104.07902">Enumeration of Latin squares with conjugate symmetry</a>, arXiv:2104.07902 [math.CO], 2021. Table 5 p. 15.
%H D. V. Zinoviev, <a href="https://www.mathnet.ru/eng/ppi2154">On the number of 1-factorizations of a complete graph</a> [in Russian], Problemy Peredachi Informatsii, 50 (No. 4), 2014, 71-78.
%H <a href="/index/To#tournament">Index entries for sequences related to tournaments</a>
%F a(n) ~ exp(2n^2 log(2n)) as n -> infinity (see CRC Handbook, p. 655, Theorem 4.20).
%Y For odd n this sequence equals A350017. Cf. A000438.
%K nonn,hard,more,nice
%O 1,4
%A _N. J. A. Sloane_
%E a(7) communicated by Vesa Linja-aho (vesa.linja-aho(AT)tkk.fi), Aug 02 2008
%E Comment, link, and update by _Charles R Greathouse IV_, May 11 2010