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%I A084546 #23 Feb 17 2023 09:10:51
%S A084546 1,1,1,1,1,3,3,1,1,6,15,20,15,6,1,1,10,45,120,210,252,210,120,45,10,1,
%T A084546 1,15,105,455,1365,3003,5005,6435,6435,5005,3003,1365,455,105,15,1,1,
%U A084546 21,210,1330,5985,20349,54264,116280,203490,293930,352716,352716,293930,203490,116280,54264,20349,5985,1330,210,21,1
%N A084546 Triangle read by rows: T(n,k) = C( C(n,2), k) for n >= 0, 0 <= k <= C(n,2).
%C A084546 T(n,k) gives number of labeled simple graphs with n nodes and k edges.
%D A084546 J. L. Gross and J. Yellen, eds., Handbook of Graph Theory, CRC Press, 2004; p. 517.
%H A084546 Alois P. Heinz, <a href="/A084546/b084546.txt">Rows n = 0..42, flattened</a>
%H A084546 R. J. Mathar, <a href="http://arxiv.org/abs/1709.09000">Statistics on Small Graphs</a>, arXiv:1709.09000 (2017) table 66.
%e A084546 Triangle begins:
%e A084546   1;
%e A084546   1;
%e A084546   1, 1;
%e A084546   1, 3,  3,  1;
%e A084546   1, 6, 15, 20, 15, 6, 1;
%e A084546   ...
%p A084546 C:= binomial:
%p A084546 T:= (n, k)-> C( C(n, 2), k):
%p A084546 seq(seq(T(n, k), k=0..C(n, 2)), n=0..10);  # _Alois P. Heinz_, Feb 17 2023
%t A084546 Table[Table[Binomial[Binomial[n,2],k],{k,0,Binomial[n,2]}],{n,1,7}]//Grid (* _Geoffrey Critzer_, Apr 28 2011 *)
%Y A084546 Cf. A083029. A subset of the rows of Pascal's triangle A007318.
%Y A084546 Cf. A006125 (row sums), A008406 (unlabeled graphs).
%K A084546 nonn,tabf
%O A084546 0,6
%A A084546 _N. J. A. Sloane_, Jul 13 2003
%E A084546 T(0,0)=1 prepended by _Alois P. Heinz_, Feb 17 2023

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