A350789 Triangle read by rows: T(n,k) is the number of unlabeled weakly connected digraphs with n arcs and k vertices, k = 1..n+1.

1, 0, 1, 0, 1, 3, 0, 0, 4, 8, 0, 0, 4, 22, 27, 0, 0, 1, 37, 108, 91, 0, 0, 1, 47, 326, 582, 350, 0, 0, 0, 38, 667, 2432, 3024, 1376, 0, 0, 0, 27, 1127, 7694, 17314, 16008, 5743, 0, 0, 0, 13, 1477, 19646, 74676, 117312, 84494, 24635

Offset: 0

Author

Andrew Howroyd, Jan 28 2022

Keywords

• nonn
• tabl

Examples

			Triangle begins:
  1;
  0, 1;
  0, 1, 3;
  0, 0, 4,  8;
  0, 0, 4, 22,   27;
  0, 0, 1, 37,  108,   91;
  0, 0, 1, 47,  326,  582,   350;
  0, 0, 0, 38,  667, 2432,  3024,  1376;
  0, 0, 0, 27, 1127, 7694, 17314, 16008, 5743;
  ...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1325 (rows 0..50)

Crossrefs

Row sums are A053454.

Column sums are A003085.

Main diagonal is A000238.

Cf. A054733 (transpose), A350450 (acyclic), A350753 (strongly connected).

Programs

PARI

\\ See A054733 for G, InvEulerMTS
T(n)={my(p=InvEulerMTS(sum(i=0, n, G(i, y+O(y^n))*x^i, O(x*x^n)))); vector(n, n, Vec(O(x^n)+polcoef(p,n-1,y)/x, -n))}
{ my(A=T(10)); for(n=1, #A, print(A[n])) }