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A000438 Number of 1-factorizations of complete graph K_{2n}. 7
1, 1, 6, 6240, 1225566720, 252282619805368320, 98758655816833727741338583040 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

REFERENCES

CRC Handbook of Combinatorial Designs (see pages 655, 720-723).

Dinitz, Jeffrey H.; Garnick, David K.; McKay, Brendan D.; There are 526,915,620 nonisomorphic one-factorizations of K_{12}. J. Combin. Des. 2 (1994), no. 4, 273-285.

N. T. Gridgeman, Latin Squares Under Restriction and a Jumboization, J. Rec. Math., 5 (1972), 198-202.

Hartman, Alan and Rosa, Alexander, Cyclic one-factorization of the complete graph. European J. Combin. 6 (1985), no. 1, 45-48.

W. D. Wallis, 1-Factorizations of complete graphs, pp. 593-631 in J. H. Dinitz and D R. Stinson, Contemporary Design Theory, Wiley, 1992.

D. V. Zinoviev, On the number of 1-factorizations of a complete graph [in Russian], Problemy Peredachi Informatsii, 50 (No. 4), 2014, 71-78.

LINKS

Table of n, a(n) for n=1..7.

Index entries for sequences related to tournaments

CROSSREFS

Cf. A000474, A003191, A035481, A035483. Equals A036981 / (2n+1)!.

Sequence in context: A111152 A202969 A003191 * A061109 A219014 A013784

Adjacent sequences:  A000435 A000436 A000437 * A000439 A000440 A000441

KEYWORD

nonn,hard,more,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

For K_16 the answer is approximately 1.48 * 10^44 and for K_18 1.52 * 10^63. - Dinitz et al.

a(7) found by Patric Ostergard and Petteri Kaski (petteri.kaski(AT)cs.helsinki.fi), Sep 19 2007

STATUS

approved

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Last modified May 23 08:43 EDT 2017. Contains 286909 sequences.