A350731 Triangle read by rows: T(n,k) is the number of strongly connected oriented graphs on n labeled nodes with k arcs, n >= 1, k=0..n*(n-1)/2.

1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 6, 36, 24, 0, 0, 0, 0, 0, 24, 480, 1940, 2970, 2040, 544, 0, 0, 0, 0, 0, 0, 120, 5040, 51330, 221910, 527940, 772080, 722250, 426420, 146160, 22320, 0, 0, 0, 0, 0, 0, 0, 720, 52920, 1026060, 8810970, 43268442, 138984510

Offset: 1

Author

Andrew Howroyd, Jan 11 2022

Keywords

• nonn
• tabf

Examples

			Triangle begins:
  [1] 1;
  [2] 0, 0;
  [3] 0, 0, 0, 2;
  [4] 0, 0, 0, 0, 6, 36,  24;
  [5] 0, 0, 0, 0, 0, 24, 480, 1940, 2970, 2040, 544;
  ...
		

Links

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

Crossrefs

Row sums are A350730.

The unlabeled version is A350750.

Cf. A057273 (digraphs), A350732 (weakly connected).

Programs

PARI

OrientedGgf(n, y=1) = {sum(k=0, n, ((1+2*y)/(1+y))^(k*(k-1)/2)*x^k/k!, O(x*x^n) )}
StrongO(n, y=1) = {my(g=serconvol(1/OrientedGgf(n,y), sum(k=0, n, x^k*(1+y)^(k*(k-1)/2), O(x*x^n)))); Vec(serlaplace(-log(g)))}
row(n)={Vecrev(StrongO(n,'y)[n], n*(n-1)/2+1)}
{ for(n=1, 6, print(row(n))) }