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%I #5 Nov 01 2018 18:22:34
%S 0,1,2,5,12,28,78,202,578,1650,4904
%N Number of non-isomorphic strict connected weight-n multiset partitions with multiset density -1.
%C The multiset density of a multiset partition is the sum of the numbers of distinct vertices in each part minus the number of parts minus the number of vertices.
%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) = 28 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}} {{1,1,2,2,2}}
%e {{1,2,3}} {{1,2,2,2}} {{1,2,2,2,2}}
%e {{1},{1,1}} {{1,2,3,3}} {{1,2,2,3,3}}
%e {{2},{1,2}} {{1,2,3,4}} {{1,2,3,3,3}}
%e {{1},{1,1,1}} {{1,2,3,4,4}}
%e {{1},{1,2,2}} {{1,2,3,4,5}}
%e {{1,2},{2,2}} {{1},{1,1,1,1}}
%e {{1,3},{2,3}} {{1,1},{1,1,1}}
%e {{2},{1,2,2}} {{1,1},{1,2,2}}
%e {{3},{1,2,3}} {{1},{1,2,2,2}}
%e {{1},{2},{1,2}} {{1,2},{2,2,2}}
%e {{1,2},{2,3,3}}
%e {{1,3},{2,3,3}}
%e {{1,4},{2,3,4}}
%e {{2},{1,1,2,2}}
%e {{2},{1,2,2,2}}
%e {{2},{1,2,3,3}}
%e {{2,2},{1,2,2}}
%e {{3},{1,2,3,3}}
%e {{3,3},{1,2,3}}
%e {{4},{1,2,3,4}}
%e {{1},{1,2},{2,2}}
%e {{1},{2},{1,2,2}}
%e {{2},{1,2},{2,2}}
%e {{2},{1,3},{2,3}}
%e {{2},{3},{1,2,3}}
%e {{3},{1,3},{2,3}}
%Y Cf. A000272, A007716, A007718, A030019, A052888, A134954, A304867, A304887, A318697, A321155, A321194, A321228, A321229, A321254.
%K nonn,more
%O 0,3
%A _Gus Wiseman_, Nov 01 2018
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