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Triangle read by rows: T(n,k) is the number of weakly connected acyclic digraphs on n unlabeled nodes with k arcs, n >= 1, k = 0..(n-1)*n/2.
9

%I #11 Jan 09 2022 13:02:59

%S 1,0,1,0,0,3,1,0,0,0,8,9,6,1,0,0,0,0,27,54,79,63,33,10,1,0,0,0,0,0,91,

%T 320,732,1136,1281,1056,649,281,85,15,1,0,0,0,0,0,0,350,1788,6012,

%U 14378,26529,38407,44621,41638,31321,18843,8983,3325,920,180,21,1

%N Triangle read by rows: T(n,k) is the number of weakly connected acyclic digraphs on n unlabeled nodes with k arcs, n >= 1, k = 0..(n-1)*n/2.

%H Andrew Howroyd, <a href="/A350449/b350449.txt">Table of n, a(n) for n = 1..1350</a> (rows 1..20)

%e Triangle begins:

%e [1] 1;

%e [2] 0, 1;

%e [3] 0, 0, 3, 1;

%e [4] 0, 0, 0, 8, 9, 6, 1;

%e [5] 0, 0, 0, 0, 27, 54, 79, 63, 33, 10, 1;

%e ...

%o (PARI) \\ See PARI link in A122078 for program code.

%o { my(T=WeakAcyclicDigraphsByArcs(6)); for(n=1, #T, print(T[n])) }

%Y Row sums are A101228.

%Y Columns sums are A350451.

%Y Leading diagonal is A000238.

%Y Cf. A350447 (not necessarily connected), A350450 (transpose).

%K nonn,tabf

%O 1,6

%A _Andrew Howroyd_, Dec 31 2021