A135388 - OEIS

%I #20 Oct 02 2024 10:11:45

%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 Max Alekseyev, <a href="/A135388/b135388.txt">Table of n, a(n) for n = 1..10</a>

%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 G. Tarry, <a href="https://www.cantab.net/users/michael.behrend/repubs/maze_maths/pages/tarry_nom.html">Géométrie de situation: Nombre de manières distinctes de parcourir en une seule course toutes les allées d'un labyrinthe rentrant, en ne passant qu'une seule fois par chacune des allées</a>, Comptes Rendus Assoc. Franç. Avance. Sci. 15, part 2 (1886), pp. 49-53.

%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).

%F a(n) = A350028(2n+1) = A357887(2n+1,n(2n+1)). - _Max Alekseyev_, Oct 19 2022

%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 Bisection of A350028.

%Y Cf. A007082, A232545, A357856, A357857, A356366, A357855, A357885, A357886, A357887.

%K nonn,walk,changed

%O 1,1

%A _Max Alekseyev_, Dec 10 2007