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A135388 Number of (directed) Eulerian circuits on the complete graph K_{2n+1}. 1

%I

%S 2,264,129976320,911520057021235200,257326999238092967427785160130560,

%T 6705710151431658873046319662156165939200000000000000,

%U 32132958735643556926111996291480203406145819659840760945049600000000000000000

%N Number of (directed) Eulerian circuits on the complete graph K_{2n+1}.

%D B. D. McKay, Applications of a technique for labeled enumeration, Congress. Numerantium, 40 (1983), 207-221.

%H Brendan D. McKay and Robert W. Robinson, <a href="http://users.cecs.anu.edu.au/~bdm/papers/euler.pdf">Asymptotic enumeration of Eulerian circuits in the complete graph</a>, Combinatorics, Probability and Computing, 7 (1998), 437-449.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CompleteGraph.html">Complete Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/EulerianCycle.html">Eulerian Cycle</a>

%F a(n) = A007082(n) * (n-1)!^(2*n+1).

%t Table[2 Length[FindEulerianCycle[CompleteGraph[2 n + 1], All]], {n, 3}] (* _Eric W. Weisstein_, Jan 09 2018 *)

%t (* a(3) requires a very large amount of memory *)

%Y Cf. A007082.

%K nonn

%O 1,1

%A _Max Alekseyev_, Dec 10 2007

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Last modified November 13 07:13 EST 2019. Contains 329085 sequences. (Running on oeis4.)