login
A135388
Number of (directed) Eulerian circuits on the complete graph K_{2n+1}.
12
2, 264, 129976320, 911520057021235200, 257326999238092967427785160130560, 6705710151431658873046319662156165939200000000000000, 32132958735643556926111996291480203406145819659840760945049600000000000000000
OFFSET
1,1
REFERENCES
B. D. McKay, Applications of a technique for labeled enumeration, Congress. Numerantium, 40 (1983), 207-221.
LINKS
Brendan D. McKay and Robert W. Robinson, Asymptotic enumeration of Eulerian circuits in the complete graph, Combinatorics, Probability and Computing, 7 (1998), 437-449.
Eric Weisstein's World of Mathematics, Complete Graph
Eric Weisstein's World of Mathematics, Eulerian Cycle
FORMULA
a(n) = A007082(n) * (n-1)!^(2*n+1).
a(n) = A350028(2n+1) = A357887(2n+1,n(2n+1)). - Max Alekseyev, Oct 19 2022
MATHEMATICA
Table[2 Length[FindEulerianCycle[CompleteGraph[2 n + 1], All]], {n, 3}] (* Eric W. Weisstein, Jan 09 2018 *)
(* a(3) requires a very large amount of memory *)
CROSSREFS
KEYWORD
nonn,walk
AUTHOR
Max Alekseyev, Dec 10 2007
STATUS
approved