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Number of non-isomorphic strict self-dual multiset partitions of weight n.
5

%I #5 Nov 13 2018 12:54:05

%S 1,1,2,4,7,14,29,57,117,240,498

%N Number of non-isomorphic strict self-dual multiset partitions of weight n.

%C Also the number of nonnegative integer symmetric matrices up to row and column permutations with sum of elements equal to n and no zero rows or columns, in which the rows (or columns) are all different.

%C The dual of a multiset partition has, for each vertex, one part consisting of the indices (or positions) of the parts containing that vertex, counted with multiplicity. For example, the dual of {{1,2},{2,2}} is {{1},{1,2,2}}.

%e Non-isomorphic representatives of the a(1) = 1 through a(5) = 14 multiset partitions:

%e {{1}} {{1,1}} {{1,1,1}} {{1,1,1,1}} {{1,1,1,1,1}}

%e {{1},{2}} {{1},{2,2}} {{1,1},{2,2}} {{1,1},{1,2,2}}

%e {{2},{1,2}} {{1},{2,2,2}} {{1,1},{2,2,2}}

%e {{1},{2},{3}} {{2},{1,2,2}} {{1,2},{1,2,2}}

%e {{1},{2},{3,3}} {{1},{2,2,2,2}}

%e {{1},{3},{2,3}} {{2},{1,2,2,2}}

%e {{1},{2},{3},{4}} {{1},{2,2},{3,3}}

%e {{1},{2},{3,3,3}}

%e {{1},{3},{2,3,3}}

%e {{2},{1,2},{3,3}}

%e {{2},{1,3},{2,3}}

%e {{1},{2},{3},{4,4}}

%e {{1},{2},{4},{3,4}}

%e {{1},{2},{3},{4},{5}}

%Y Cf. A000219, A007716, A045778, A059201, A316980, A316983, A319560, A319616.

%Y Cf. A320796, A320797, A321402, A321405, A321406, A321407.

%K nonn,more

%O 0,3

%A _Gus Wiseman_, Nov 09 2018