A357886 Triangle read by rows: T(n,k) = number of open trails of length k starting and ending at fixed distinct vertices in the complete undirected graph on n labeled vertices, for n >= 1 and k = 0 .. n*(n-1)/2.

0, 0, 1, 0, 1, 1, 0, 0, 1, 2, 2, 4, 6, 0, 0, 1, 3, 6, 18, 48, 78, 96, 132, 132, 0, 0, 1, 4, 12, 48, 180, 528, 1392, 3600, 7920, 13680, 21840, 31872, 25008, 0, 0, 0, 1, 5, 20, 100, 480, 1980, 7680, 29040, 100920, 316320, 923520, 2502000, 6011760, 12584880, 23417280, 38196480, 50112000, 53667840, 64988160, 64988160, 0

Offset: 1

Author

Max Alekseyev, Oct 19 2022

Keywords

• tabf
• nonn
• walk

Examples

			Triangle T(n,k) starts with:
n=1: 0,
n=2: 0, 1,
n=3: 0, 1, 1, 0,
n=4: 0, 1, 2, 2, 4, 6, 0,
n=5: 0, 1, 3, 6, 18, 48, 78, 96, 132, 132, 0,
...
		

Links

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

Crossrefs

Cf. A007082, A135388, A232545, A350028, A357855, A357856 (row sums), A357857, A356366, A357885, A357887.