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Number of non-isomorphic strict multiset partitions of weight n with no equivalent vertices.
5

%I #6 Jul 18 2018 17:51:43

%S 1,1,2,6,15,40,121

%N Number of non-isomorphic strict multiset partitions of weight n with no equivalent vertices.

%C Also the number of nonnegative integer n X n matrices with sum of elements equal to n, under row and column permutations, with no equal rows and no equal columns.

%C In a multiset partition, two vertices are equivalent if in every block the multiplicity of the first is equal to the multiplicity of the second.

%e Non-isomorphic representatives of the a(3) = 6 strict multiset partitions with no equivalent vertices (first column) and their duals (second column):

%e (111) <-> (111)

%e (122) <-> (1)(11)

%e (1)(11) <-> (122)

%e (1)(22) <-> (1)(22)

%e (2)(12) <-> (2)(12)

%e (1)(2)(3) <-> (1)(2)(3)

%Y Cf. A000009, A001055, A007716, A007717, A020555, A045778.

%Y Cf. A316974, A316978, A316979, A316980, A316983.

%K nonn,more

%O 0,3

%A _Gus Wiseman_, Jul 18 2018