A350793 Triangle read by rows: T(n,k) is the number of digraphs on n labeled nodes with k arcs and a global source (or sink), n >= 1, k = 0..(n-1)^2.

1, 0, 2, 0, 0, 9, 12, 3, 0, 0, 0, 64, 252, 396, 320, 144, 36, 4, 0, 0, 0, 0, 625, 4860, 17060, 35900, 50775, 51300, 38340, 21540, 9075, 2800, 600, 80, 5, 0, 0, 0, 0, 0, 7776, 99720, 603720, 2300310, 6206730, 12654384, 20310840, 26385240, 28273620, 25302960

Offset: 1

Author

Andrew Howroyd, Jan 17 2022

Keywords

• nonn
• tabf

Examples

			Triangle begins:
  [1] 1;
  [2] 0, 2;
  [3] 0, 0, 9, 12, 3;
  [4] 0, 0, 0, 64, 252, 396, 320, 144, 36, 4;
  ...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..2490 (rows 1..20)

Crossrefs

Row sums are A350792.

The leading diagonal is A000169.

The unlabeled version is A350797.

Cf. A057274, A350791.

Programs

PARI

InitiallyV(n, e=2)={my(v=vector(n)); for(n=1, n, v[n] = n*e^((n-1)^2) - sum(k=1, n-1, binomial(n,k)*e^((n-2)*(n-k))*v[k])); v}
row(n)={Vecrev(InitiallyV(n, 1+'y)[n])}
{ for(n=1, 5, print(row(n))) }