A350610 Irregular triangle read by rows: T(n,k) (n >= 1, 0 <= k <= (n-1)*(n-2)/2) = number of weakly connected subdigraphs of the transitive tournament on n nodes that have k arcs.

1, 1, 1, 3, 1, 6, 15, 9, 1, 10, 45, 120, 162, 109, 27, 1, 15, 105, 455, 1365, 2755, 3738, 3353, 1889, 600, 81, 1, 21, 210, 1330, 5985, 20349, 52764, 104726, 159351, 185155, 162455, 105436, 48881, 15255, 2862, 243, 1, 28, 378, 3276, 20475, 98280, 376740, 1173564, 2995480, 6295857, 10925190, 15658609, 18498220, 17926289, 14138445, 8968823, 4498534, 1740117, 499834, 100225, 12501, 729

Offset: 1

Author

Don Knuth, Jan 16 2022

Keywords

• nonn
• tabf

Comments

The sum of row n is A350608(n).

For references and links see A350608.

Examples

			For example, when n=4, the 31 weakly connected graphs have respectively 1, 6, 15, 9 cases with 0, 1, 2, and 3 arcs (as in the example given for A350608).
Triangle T(n,k) begins:
  1;
  1;
  1,  3;
  1,  6,  15,   9;
  1, 10,  45, 120,  162,  109,   27;
  1, 15, 105, 455, 1365, 2755, 3738, 3353, 1889, 600, 81;
  ...
		

Links

• Don Knuth, Rows n = 1..16, flattened
• Don Knuth, The first 16 rows.

Crossrefs

Cf. A350608, A350609.