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A357855
Number of closed trails starting and ending at a fixed vertex in the complete undirected graph on n labeled vertices.
9
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.
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.
KEYWORD
nonn,more,walk
AUTHOR
Max Alekseyev, Oct 16 2022
EXTENSIONS
a(9) from Bert Dobbelaere, Oct 17 2022
STATUS
approved