A316892 Number of non-isomorphic strict multiset partitions of {1, 1, 2, 2, 3, 3, ..., n, n} with no equivalent vertices.

1, 1, 3, 9, 24, 69, 211, 654

Offset: 0

Author

Gus Wiseman, Jul 18 2018

Keywords

• nonn
• more

Comments

Also the number of unlabeled graphs with n edges, allowing loops, with no equivalent vertices (two vertices are equivalent if in every edge the multiplicity of the first is equal to the multiplicity of the second). For example, non-isomorphic representatives of the a(2) = 3 multigraphs are {(1,2),(1,3)}, {(1,1),(1,2)}, {(1,1),(2,2)}.

Examples

			Non-isomorphic representatives of the a(3) = 9 strict multiset partitions:
  (112)(233)
  (1)(2)(1233)
  (1)(12)(233)
  (2)(11)(233)
  (11)(22)(33)
  (12)(13)(23)
  (1)(2)(3)(123)
  (1)(2)(12)(33)
  (1)(2)(13)(23)
		

Crossrefs

Cf. A007716, A007717, A020555, A050535, A053419, A094574, A316974.

Extensions

a(6)-a(7) from Andrew Howroyd, Feb 07 2020