A357885 Triangle read by rows: T(n,k) = number of closed trails of length k starting and ending at a fixed vertex in the complete undirected graph on n labeled vertices, for n >= 1 and k = 0 .. n(n-1)/2.

1, 1, 0, 1, 0, 0, 2, 1, 0, 0, 6, 6, 0, 0, 1, 0, 0, 12, 24, 24, 72, 168, 0, 0, 528, 1, 0, 0, 20, 60, 120, 480, 1680, 3120, 5760, 15840, 29040, 22320, 0, 0, 0, 1, 0, 0, 30, 120, 360, 1800, 8280, 27360, 88560, 310320, 934560, 2296800, 5541120, 12965760, 21837600, 27740160, 58752000, 101882880, 0, 0, 389928960

Offset

1,7

Links

Max Alekseyev, Table of m, a(m) for m = 1..129 (rows n = 1..9)

Formula

For k >= 1, T(n,k) = A357887(n,k) * k / n.

Example

Triangle starts:
n=1: 1
n=2: 1, 0
n=3: 1, 0, 0, 2
n=4: 1, 0, 0, 6, 6, 0, 0
n=5: 1, 0, 0, 12, 24, 24, 72, 168, 0, 0, 528
...

Crossrefs

Cf. A007082, A135388, A232545, A350028, A356366, A357855 (row sums), A357856, A357857, A357886, A357887.

Sequence in context: A105868 A371568 A267163 * A265163 A057275 A057271

Adjacent sequences: A357882 A357883 A357884 * A357886 A357887 A357888

Keyword

tabf,nonn,walk

Author

Max Alekseyev, Oct 18 2022

Status

approved