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Number of non-isomorphic strict multiset partitions of {1, 1, 2, 2, 3, 3, ..., n, n}.
15

%I #12 Feb 07 2020 19:33:54

%S 1,1,4,14,49,173,652,2494

%N Number of non-isomorphic strict multiset partitions of {1, 1, 2, 2, 3, 3, ..., n, n}.

%C Also the number of unlabeled multigraphs with n edges, allowing loops, spanning an initial interval of positive integers 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) = 4 multigraphs are {(1,2),(1,3)}, {(1,1),(1,2)}, {(1,1),(2,2)}, {(1,1),(1,1)}.

%e Non-isomorphic representatives of the a(3) = 14 strict multiset partitions:

%e (112233),

%e (1)(12233), (11)(2233), (12)(1233), (112)(233),

%e (1)(2)(1233), (1)(12)(233), (1)(23)(123), (2)(11)(233), (11)(22)(33), (12)(13)(23),

%e (1)(2)(3)(123), (1)(2)(12)(33), (1)(2)(13)(23).

%Y Cf. A001055, A007716, A007717, A007719, A020554, A020555, A045778, A050535, A053419, A061742, A094574, A162247, A316892, A316972.

%K nonn,more

%O 0,3

%A _Gus Wiseman_, Jul 17 2018

%E a(7) from _Andrew Howroyd_, Feb 07 2020