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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.

%I A357886 #14 Oct 22 2022 08:08:02
%S A357886 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,
%T A357886 48,180,528,1392,3600,7920,13680,21840,31872,25008,0,0,0,1,5,20,100,
%U A357886 480,1980,7680,29040,100920,316320,923520,2502000,6011760,12584880,23417280,38196480,50112000,53667840,64988160,64988160,0
%N 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.
%H A357886 Max Alekseyev, <a href="/A357886/b357886.txt">Table of m, a(m) for m = 1..129</a> (rows n = 1..9)
%e A357886 Triangle T(n,k) starts with:
%e A357886 n=1: 0,
%e A357886 n=2: 0, 1,
%e A357886 n=3: 0, 1, 1, 0,
%e A357886 n=4: 0, 1, 2, 2, 4, 6, 0,
%e A357886 n=5: 0, 1, 3, 6, 18, 48, 78, 96, 132, 132, 0,
%e A357886 ...
%Y A357886 Cf. A007082, A135388, A232545, A350028, A357855, A357856 (row sums), A357857, A356366, A357885, A357887.
%K A357886 tabf,nonn,walk
%O A357886 1,10
%A A357886 _Max Alekseyev_, Oct 19 2022