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.

1, 0, 2, 0, 0, 12, 8, 0, 0, 0, 128, 240, 192, 64, 0, 0, 0, 0, 2000, 7104, 13120, 15360, 11520, 5120, 1024, 0, 0, 0, 0, 0, 41472, 234240, 729600, 1578240, 2531840, 3068928, 2795520, 1863680, 860160, 245760, 32768

Offset: 1

Author

Andrew Howroyd, Jan 11 2022

Keywords

• nonn
• tabf

Examples

			Triangle begins:
  [1] 1;
  [2] 0, 2;
  [3] 0, 0, 12,   8;
  [4] 0, 0,  0, 128,  240,  192,    64;
  [5] 0, 0,  0,   0, 2000, 7104, 13120, 15360, 11520, 5120, 1024;
  ...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1350 (rows 1..20)

Crossrefs

Row sums are A054941.

The leading diagonal is A097629.

The unlabeled version is A350734.

Cf. A062735 (digraphs), A350731 (strongly connected).

Programs

PARI

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))}
{ for(n=1, 5, print(row(n))) }