A350749 Triangle read by rows: T(n,k) is the number of oriented graphs on n labeled nodes with k arcs, n >= 0, k = 0..n*(n-1)/2.

1, 1, 1, 2, 1, 6, 12, 8, 1, 12, 60, 160, 240, 192, 64, 1, 20, 180, 960, 3360, 8064, 13440, 15360, 11520, 5120, 1024, 1, 30, 420, 3640, 21840, 96096, 320320, 823680, 1647360, 2562560, 3075072, 2795520, 1863680, 860160, 245760, 32768

Offset

0,4

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1350 (rows 0..20)

Formula

T(n,k) = 2^k * binomial(n*(n-1)/2, k) = A013609(n*(n-1)/2, k).

T(n,k) = [y^k] (1+2*y)^(n*(n-1)/2).

Example

Triangle begins:
  [0] 1;
  [1] 1;
  [2] 1,  2;
  [3] 1,  6,  12,   8;
  [4] 1, 12,  60, 160,  240,  192,    64;
  [5] 1, 20, 180, 960, 3360, 8064, 13440, 15360, 11520, 5120, 1024;
  ...

Prog

(PARI) T(n, k) = 2^k * binomial(n*(n-1)/2, k)
(PARI)
row(n) = {Vecrev((1+2*y)^(n*(n-1)/2))}
{ for(n=0, 6, print(row(n))) }

Crossrefs

Row sums are A047656.

The unlabeled version is A350733.

Cf. A013609, A350732 (weakly connected), A350731 (strongly connected).

Sequence in context: A342589 A325635 A081064 * A347594 A128534 A002562

Adjacent sequences: A350746 A350747 A350748 * A350750 A350751 A350752

Keyword

nonn,tabf

Author

Andrew Howroyd, Feb 15 2022

Status

approved