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A084546 Triangle read by rows: T(n,k) = C( C(n,2), k) for n >= 1, 0 <= k <= C(n,2). 11
1, 1, 1, 1, 3, 3, 1, 1, 6, 15, 20, 15, 6, 1, 1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1, 1, 15, 105, 455, 1365, 3003, 5005, 6435, 6435, 5005, 3003, 1365, 455, 105, 15, 1, 1, 21, 210, 1330, 5985, 20349, 54264, 116280, 203490, 293930, 352716, 352716, 293930, 203490, 116280, 54264, 20349, 5985, 1330, 210, 21, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

T(n,k) gives number of labeled simple graphs with n nodes and k edges.

REFERENCES

J. L. Gross and J. Yellen, eds., Handbook of Graph Theory, CRC Press, 2004; p. 517.

LINKS

Table of n, a(n) for n=1..63.

R. J. Mathar, Statistics on Small Graphs, arXiv:1709.09000 (2017) table 66.

EXAMPLE

Triangle begins

1;

1,1;

1,3,3,1;

1,6,15,20,15,6,1; ...

MATHEMATICA

Table[Table[Binomial[Binomial[n, 2], k], {k, 0, Binomial[n, 2]}], {n, 1, 7}]//Grid (* Geoffrey Critzer, Apr 28 2011 *)

CROSSREFS

Cf. A083029. A subset of the rows of Pascal's triangle A007318.

Cf. A006125 (row sums), A008406 (unlabeled graphs).

Sequence in context: A080858 A144228 A083029 * A288266 A174116 A270273

Adjacent sequences:  A084543 A084544 A084545 * A084547 A084548 A084549

KEYWORD

nonn,tabf

AUTHOR

N. J. A. Sloane, Jul 13 2003

STATUS

approved

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Last modified February 18 15:33 EST 2018. Contains 299324 sequences. (Running on oeis4.)