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%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
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