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Triangle read by rows: T(n,k) is the number of unlabeled weakly connected acyclic digraphs with n arcs and k vertices, n >= 0, k = 1..n+1.
7

%I #9 Jan 09 2022 13:10:19

%S 1,0,1,0,0,3,0,0,1,8,0,0,0,9,27,0,0,0,6,54,91,0,0,0,1,79,320,350,0,0,

%T 0,0,63,732,1788,1376,0,0,0,0,33,1136,6012,9933,5743,0,0,0,0,10,1281,

%U 14378,45225,54502,24635,0,0,0,0,1,1056,26529,151848,322736,298250,108968

%N Triangle read by rows: T(n,k) is the number of unlabeled weakly connected acyclic digraphs with n arcs and k vertices, n >= 0, k = 1..n+1.

%H Andrew Howroyd, <a href="/A350450/b350450.txt">Table of n, a(n) for n = 0..860</a> (rows 0..40)

%e Triangle begins:

%e 1;

%e 0, 1;

%e 0, 0, 3;

%e 0, 0, 1, 8;

%e 0, 0, 0, 9, 27;

%e 0, 0, 0, 6, 54, 91;

%e 0, 0, 0, 1, 79, 320, 350;

%e 0, 0, 0, 0, 63, 732, 1788, 1376;

%e 0, 0, 0, 0, 33, 1136, 6012, 9933, 5743;

%e ...

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

%o { my(T=WeakAcyclicDigraphsTr(10)); for(n=1, #T, print(T[n])); }

%Y Main diagonal is A000238.

%Y Row sums are A350451.

%Y Column sums are A101228.

%Y Cf. A122078, A350449 (transpose).

%K nonn,tabl

%O 0,6

%A _Andrew Howroyd_, Dec 31 2021