A123554 Triangle read by rows: T(n,k) = number of labeled loopless digraphs with n nodes and k arcs (n >= 1, 0 <= k <= n*(n-1)).

1, 1, 2, 1, 1, 6, 15, 20, 15, 6, 1, 1, 12, 66, 220, 495, 792, 924, 792, 495, 220, 66, 12, 1, 1, 20, 190, 1140, 4845, 15504, 38760, 77520, 125970, 167960, 184756, 167960, 125970, 77520, 38760, 15504, 4845, 1140, 190, 20, 1, 1, 30, 435, 4060, 27405, 142506, 593775

Offset

1,3

References

J. L. Gross and J. Yellen, eds., Handbook of Graph Theory, CRC Press, 2004; p. 521.

Links

G. C. Greubel, Table of n, a(n) for the first 25 rows, flattened

Formula

T(n,k) = binomial(n*(n-1), k). - Andrew Howroyd, Apr 19 2020

Example

Triangle begins:
1
1 2 1
1 6 15 20 15 6 1
1 12 66 220 495 792 924 792 495 220 66 12 1

Mathematica

Table[CoefficientList[Series[(1+x)^(2*Binomial[n, 2]), {x, 0, 2*Binomial[n, 2]}], x], {n, 6}] (* Geoffrey Critzer, Nov 12 2011 *)

Prog

(PARI) T(n, k)={binomial(n*(n-1), k)}
{for(n=1, 5, for(k=0, n*(n-1), print1(T(n, k), ", ")); print)} \\ Andrew Howroyd, Apr 19 2020

Crossrefs

Row sums are A053763.

Cf. A052283 (unlabeled analog).

Sequence in context: A165891 A039763 A094262 * A105291 A214631 A025270

Adjacent sequences: A123551 A123552 A123553 * A123555 A123556 A123557

Keyword

nonn,tabf

Author

N. J. A. Sloane, Nov 15 2006

Extensions

More terms from Vladeta Jovovic, Nov 15 2006

Status

approved