A356366 Number of (directed) circuits in the complete undirected graph on n labeled vertices.

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

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..9.

Formula

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.

Example

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).

Crossrefs

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

Sequence in context: A197855 A289126 A062097 * A323706 A125765 A068873

Adjacent sequences: A356363 A356364 A356365 * A356367 A356368 A356369

Keyword

nonn,more,walk

Author

Max Alekseyev, Oct 16 2022

Extensions

a(9) from Bert Dobbelaere, Oct 17 2022

Status

approved