A356366 - OEIS

%I #40 Oct 19 2022 07:09:30

%S 1,2,5,18,523,44884,227838935,1086696880188,1566338449874827101

%N Number of (directed) circuits in the complete undirected graph on n labeled vertices.

%C In other words, number of closed trails up to cyclic rotations (cf. A357855).

%F a(n) = Sum_{k = 0..n(n-1)/2} A357887(n,k) = n + n * Sum_{k = 1..n(n-1)/2} A357885(n,k) / k.

%e For n = 3, we have 5 circuits: 3 of length 0 (singleton vertices), and 2 of length 3 (1->2->3->1 and 1->3->2->1).

%Y Cf. A007082, A135388, A232545, A350028, A357855, A357856, A357857, A357885, A357886, A357887.

%K nonn,more,walk

%O 1,2

%A _Max Alekseyev_, Oct 16 2022

%E a(9) from _Bert Dobbelaere_, Oct 17 2022