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A350732 Triangle read by rows: T(n,k) is the number of weakly connected oriented graphs on n labeled nodes with k arcs, n >= 0, k=0..n*(n-1)/2.

%I A350732 #8 Jan 16 2022 17:46:14
%S A350732 1,0,2,0,0,12,8,0,0,0,128,240,192,64,0,0,0,0,2000,7104,13120,15360,
%T A350732 11520,5120,1024,0,0,0,0,0,41472,234240,729600,1578240,2531840,
%U A350732 3068928,2795520,1863680,860160,245760,32768
%N A350732 Triangle read by rows: T(n,k) is the number of weakly connected oriented graphs on n labeled nodes with k arcs, n >= 0, k=0..n*(n-1)/2.
%H A350732 Andrew Howroyd, <a href="/A350732/b350732.txt">Table of n, a(n) for n = 1..1350</a> (rows 1..20)
%e A350732 Triangle begins:
%e A350732   [1] 1;
%e A350732   [2] 0, 2;
%e A350732   [3] 0, 0, 12,   8;
%e A350732   [4] 0, 0,  0, 128,  240,  192,    64;
%e A350732   [5] 0, 0,  0,   0, 2000, 7104, 13120, 15360, 11520, 5120, 1024;
%e A350732   ...
%o A350732 (PARI)
%o A350732 row(n)={Vecrev(n!*polcoef(1 + log(sum(k=0, n, (1+2*y)^(k*(k-1)/2)*x^k/k!, O(x*x^n))), n))}
%o A350732 { for(n=1, 5, print(row(n))) }
%Y A350732 Row sums are A054941.
%Y A350732 The leading diagonal is A097629.
%Y A350732 The unlabeled version is A350734.
%Y A350732 Cf. A062735 (digraphs), A350731 (strongly connected).
%K A350732 nonn,tabf
%O A350732 1,3
%A A350732 _Andrew Howroyd_, Jan 11 2022