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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, 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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 23 15:06 EDT 2020. Contains 337310 sequences. (Running on oeis4.)