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Table of graphs with n (>=0) nodes and k (>=0) edges. Each type of object labeled from its own label set.
2

%I #10 Feb 14 2023 20:56:12

%S 1,1,1,1,1,3,6,6,1,6,30,120,360,720,720,1,10,90,720,5040,30240,151200,

%T 604800,1814400,3628800,3628800,1,15,210,2730,32760,360360,3603600,

%U 32432400,259459200,1816214400,10897286400,54486432000,217945728000,653837184000,1307674368000,1307674368000

%N Table of graphs with n (>=0) nodes and k (>=0) edges. Each type of object labeled from its own label set.

%D F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, p. 114 (2.4.44).

%F a(n, k) = k!*binomial(binomial(n, 2), k).

%e 1;

%e 1;

%e 1, 1;

%e 1, 3, 6, 6;

%e 1, 6, 30, 120, 360, 720, 720;

%e ...

%Y Row sums: A091479.

%Y Row lengths: A000124(n-1) for n>=1.

%Y Columns 0-2: A000012, A000217(n-1), A033487(n-2).

%Y a(n,A000217(n-1)) = A052295(n-1).

%Y Cf. A006125, A008406.

%K nonn,tabf

%O 0,6

%A _Christian G. Bower_, Jan 13 2004

%E T(0,0)=1 prepended by _Alois P. Heinz_, Feb 14 2023