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

0,6

References

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

Links

Table of n, a(n) for n=0..41.

Formula

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

Example

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

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.

Sequence in context: A285628 A319886 A021736 * A239567 A198239 A086727

Adjacent sequences: A091475 A091476 A091477 * A091479 A091480 A091481

Keyword

nonn,tabf

Author

Christian G. Bower, Jan 13 2004

Extensions

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

Status

approved