A126066 Triangle read by rows: T(n,k) is the number of unlabeled digraphs on n nodes with k arcs up to reversing the arcs, k=0..n*(n-1).

1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 1, 1, 1, 1, 4, 9, 18, 24, 30, 24, 18, 9, 4, 1, 1, 1, 1, 4, 11, 38, 89, 210, 382, 616, 787, 880, 787, 616, 382, 210, 89, 38, 11, 4, 1, 1, 1, 1, 4, 12, 48, 165, 567, 1703, 4623, 10836, 22273, 39866, 62650, 86209, 104456, 111256, 104456, 86209, 62650, 39866, 22273, 10836, 4623, 1703, 567, 165, 48, 12, 4, 1, 1

Offset: 0

Author

Vladeta Jovovic, Feb 28 2007

Keywords

• nonn
• tabf

Examples

			Triangle begins:
  1;
  1;
  1,1,1;
  1,1,3,3,3,1,1;
  1,1,4,9,18,24,30,24,18,9,4,1,1;
  ...
G.f. for fourth row is obtained if we set x(i) = 1+x^i, i=1..12 in (1/48)*(x(1)^12+12*x(1)^2*x(2)^5+4*x(2)^6+8*x(3)^4+12*x(4)^3+3*x(1)^4*x(2)^4+8*x(6)^2)
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..2680 (rows 0..20)

Crossrefs

Row sums give A054933.

Cf. A052283, A126066.

Formula

T(n,k) = (A052283(n,k) + A126066(n,k))/2. - Andrew Howroyd, Apr 20 2020

Extensions

a(0)=1 prepended and terms a(64) and beyond from Andrew Howroyd, Apr 20 2020