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%I #4 Nov 20 2018 12:20:49
%S 1,1,2,4,9,17,42,92,231,579,1577
%N Number of non-isomorphic weight-n multiset partitions whose part-sizes are also their vertex-degrees.
%C Also the number of nonnegative integer square matrices up to row and column permutations with sum of elements equal to n and no zero rows or columns, with the same multiset of row sums as of column sums.
%C The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices.
%e Non-isomorphic representatives of the a(1) = 1 through a(5) = 17 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},{1,2}} {{1,1},{2,2,2}}
%e {{1},{2},{3}} {{1},{2,2,2}} {{1,2},{1,2,2}}
%e {{2},{1,2,2}} {{1},{2,2,2,2}}
%e {{1},{1},{2,3}} {{2},{1,2,2,2}}
%e {{1},{2},{3,3}} {{1},{2,2},{3,3}}
%e {{1},{3},{2,3}} {{1},{2,3},{2,3}}
%e {{1},{2},{3},{4}} {{1},{2},{3,3,3}}
%e {{1},{3},{2,3,3}}
%e {{2},{1,2},{3,3}}
%e {{2},{1,3},{2,3}}
%e {{3},{3},{1,2,3}}
%e {{1},{2},{2},{3,4}}
%e {{1},{2},{3},{4,4}}
%e {{1},{2},{4},{3,4}}
%e {{1},{2},{3},{4},{5}}
%Y Cf. A000700, A007716, A057150, A120732, A319056, A319616, A320451, A321719, A321721, A321722, A321724, A321732, A321733, A321735, A321739.
%K nonn,more
%O 0,3
%A _Gus Wiseman_, Nov 19 2018
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