A283753 Irregular triangular array read by rows: T(n,k) is the number of non-isomorphic unlabeled weakly connected digraphs on n nodes and with k arcs.

1, 1, 1, 3, 4, 4, 1, 1, 8, 22, 37, 47, 38, 27, 13, 5, 1, 1, 27, 108, 326, 667, 1127, 1477, 1665, 1489, 1154, 707, 379, 154, 61, 16, 5, 1, 1, 91, 582, 2432, 7694, 19646, 42148, 77305, 122953, 170315, 206982, 220768, 207301, 171008, 124110, 78813, 43862, 21209, 8951, 3242, 1043, 288, 76, 17, 5, 1, 1, 350, 3024, 17314, 74676, 266364, 808620, 2144407

Offset: 1

Author

Marko Riedel, Mar 15 2017

Keywords

• nonn
• tabf

Comments

The range for the subindex k is from n-1 to n(n-1).

Obtained from A054733 by removing leading zeros.

Examples

			First rows are:
1;
1,    1;
3,    4,   4,   1,    1;
8,   22,  37,  47,   38,   27,   13,    5,    1,   1;
27, 108, 326, 667, 1127, 1477, 1665, 1489, 1154, 707, 379, ...
		

References

• E. Palmer and F. Harary, Graphical Enumeration, Academic Press, 1973.

Links

• Marko R. Riedel, Number of distinct connected digraphs
• Marko Riedel, Maple code for sequences A052283, A283753.

Crossrefs

Cf. A000273, A000238, A003085, A052283.

Programs

PARI

\\ See A054733 for G, InvEulerMTS.
row(n)={Vecrev(polcoef(InvEulerMTS(sum(i=0, n, G(i, y)*x^i, O(x*x^n))), n)/y^(n-1))}
{ for(n=1, 6, print(row(n))) } \\ Andrew Howroyd, Jan 28 2022