A091478 Table of graphs with n (>=0) nodes and k (>=0) edges. Each type of object labeled from its own label set.

1, 1, 1, 1, 1, 3, 6, 6, 1, 6, 30, 120, 360, 720, 720, 1, 10, 90, 720, 5040, 30240, 151200, 604800, 1814400, 3628800, 3628800, 1, 15, 210, 2730, 32760, 360360, 3603600, 32432400, 259459200, 1816214400, 10897286400, 54486432000, 217945728000, 653837184000, 1307674368000, 1307674368000

Offset: 0

Author

Christian G. Bower, Jan 13 2004

Keywords

• nonn
• tabf

Examples

			  1;
  1;
  1, 1;
  1, 3,  6,   6;
  1, 6, 30, 120, 360, 720, 720;
  ...
		

References

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

Crossrefs

Row sums: A091479.

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

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

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

Cf. A006125, A008406.

Formula

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

Extensions

T(0,0)=1 prepended by Alois P. Heinz, Feb 14 2023