%I #17 Oct 21 2022 14:31:54

%S 1,2,0,3,0,0,2,4,0,0,8,6,0,0,5,0,0,20,30,24,60,120,0,0,264,6,0,0,40,

%T 90,144,480,1440,2340,3840,9504,15840,11160,0,0,0,7,0,0,70,210,504,

%U 2100,8280,23940,68880,217224,594720,1339800,2983680,6482880,10190880,12136320,24192000,39621120,0,0,129976320

%N Triangle read by rows: T(n,k) = number of circuits of length k in the complete undirected graph on n labeled vertices, for n >= 1 and k = 0 .. n(n-1)/2.

%H Max Alekseyev, <a href="/A357887/b357887.txt">Table of m, a(m) for m = 1..129</a> (rows n=1..9)

%F For k >= 1, T(n,k) = A357885(n,k) * n / k.

%F Last nonzero element in row n:

%F T(2n+1,n(2n+1)) = A135388(n) = A350028(2n+1) = A007082(n) * (n-1)!^(2*n+1);

%F T(2n,2n(n-1)) = A350028(2n) * (2n-1)!!.

%e Triangle T(n,k) starts with:

%e n=1: 1,

%e n=2: 2, 0,

%e n=3: 3, 0, 0, 2,

%e n=4: 4, 0, 0, 8, 6, 0, 0,

%e n=5: 5, 0, 0, 20, 30, 24, 60, 120, 0, 0, 264,

%e ...

%Y Cf. A007082, A135388, A232545, A350028, A356366 (row sums), A357855, A357856, A357857, A357885, A357886.

%K tabf,nonn,walk

%O 1,2

%A _Max Alekseyev_, Oct 19 2022