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%I #4 Aug 15 2019 07:30:18
%S 1,1,2,4,9,19,49,115,310,830,2383
%N Number of non-isomorphic multiset partitions of weight n where every vertex, as a multiset of weight 1, is the multiset-meet of some subset of the edges.
%C The multiset-meet of a collection of multisets has as underlying set the intersection of their underlying sets and as multiplicities the minima of their multiplicities.
%e Non-isomorphic representatives of the a(1) = 1 through a(5) = 19 multiset partitions:
%e {1} {1}{1} {1}{11} {1}{111} {1}{1111}
%e {1}{2} {1}{1}{1} {1}{1}{11} {1}{1}{111}
%e {1}{2}{2} {1}{2}{12} {1}{11}{11}
%e {1}{2}{3} {1}{2}{22} {1}{12}{22}
%e {1}{1}{1}{1} {1}{2}{122}
%e {1}{1}{2}{2} {1}{2}{222}
%e {1}{2}{2}{2} {1}{1}{1}{11}
%e {1}{2}{3}{3} {1}{1}{2}{22}
%e {1}{2}{3}{4} {1}{2}{2}{12}
%e {1}{2}{2}{22}
%e {1}{2}{3}{23}
%e {1}{2}{3}{33}
%e {1}{1}{1}{1}{1}
%e {1}{1}{2}{2}{2}
%e {1}{2}{2}{2}{2}
%e {1}{2}{2}{3}{3}
%e {1}{2}{3}{3}{3}
%e {1}{2}{3}{4}{4}
%e {1}{2}{3}{4}{5}
%Y Cf. A007716, A059523, A326961, A326965, A326967, A326972, A326974, A326976, A326977, A326979, A327012.
%K nonn,more
%O 0,3
%A _Gus Wiseman_, Aug 15 2019
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