A357855 Number of closed trails starting and ending at a fixed vertex in the complete undirected graph on n labeled vertices.

1, 1, 3, 13, 829, 78441, 622316671, 3001764349333, 5926347237626029593

Offset

1,3

Comments

Trails are directed and pass through each (undirected) edge at most once in either of the two directions.

Links

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

Formula

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

Example

For n = 3, we have a(3) = 3 trails starting and ending at vertex 1: 1 (single vertex), 1->2->3->1, and 1->3->2->1.

Crossrefs

Cf. A007082, A135388, A232545, A350028, A356366, A357856, A357857, A357885, A357886, A357887.

Sequence in context: A089711 A173759 A001039 * A368297 A065831 A092540

Adjacent sequences: A357852 A357853 A357854 * A357856 A357857 A357858

Keyword

nonn,more,walk

Author

Max Alekseyev, Oct 16 2022

Extensions

a(9) from Bert Dobbelaere, Oct 17 2022

Status

approved