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A356366
Number of (directed) circuits in the complete undirected graph on n labeled vertices.
9
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).
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).
KEYWORD
nonn,more,walk
AUTHOR
Max Alekseyev, Oct 16 2022
EXTENSIONS
a(9) from Bert Dobbelaere, Oct 17 2022
STATUS
approved