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A316892
Number of non-isomorphic strict multiset partitions of {1, 1, 2, 2, 3, 3, ..., n, n} with no equivalent vertices.
2
1, 1, 3, 9, 24, 69, 211, 654
OFFSET
0,3
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)}.
EXAMPLE
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)
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jul 18 2018
EXTENSIONS
a(6)-a(7) from Andrew Howroyd, Feb 07 2020
STATUS
approved