%I #25 Apr 15 2021 20:25:32
%S 1,1,3,1,3,16,15,6,1,30,135,222,205,120,45,10,1,15,330,1581,3760,5715,
%T 6165,4945,2997,1365,455,105,15,1,315,4410,23604,73755,159390,259105,
%U 331716,343161,290745,202755,116175,54257,20349,5985,1330,210,21,1
%N Triangle T(m, n) = the number of point-labeled graphs with n points and m edges, no points isolated. By rows, n >= 0, ceiling(n/2) <= m <= binomial(n,2).
%C The row sums are A006129, omitting row 1 and A006129(1).
%H David Pasino, <a href="/A276639/b276639.txt">Table of n, a(n) for n = 1..512</a>
%F T(n, m) = Sum_{k=0,..n} binomial(n, k) * (-1)^(n-k) * A084546(k, m).
%e Triangle T(n, m) begins:
%e n/m 0 1 2 3 4 5 6 7 8 9 10
%e 0 1 0 0 0 0 0 0 0 0 0 0
%e 1 0 0 0 0 0 0 0 0 0 0 0
%e 2 0 1 0 0 0 0 0 0 0 0 0
%e 3 0 0 3 1 0 0 0 0 0 0 0
%e 4 0 0 3 16 15 6 1 0 0 0 0
%e 5 0 0 0 30 135 222 205 120 45 10 1
%t Table[Sum[Binomial[n, k] (-1)^(n - k) Binomial[Binomial[k, 2], m], {k, 0, n}], {n, 7}, {m, Ceiling[n/2], Binomial[n, 2]}] /. {} -> {1} // Flatten (* _Michael De Vlieger_, Sep 19 2016 *)
%Y Another version is A054548.
%K nonn,tabf
%O 1,3
%A _David Pasino_, Sep 08 2016
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