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%I A330668 #8 Apr 27 2020 09:43:41
%S A330668 1,1,1,3,22,204,2953
%N A330668 Number of non-isomorphic balanced reduced multisystems of weight n whose leaves (which are multisets of atoms) are all sets.
%C A330668 A balanced reduced multisystem is either a finite multiset, or a multiset partition with at least two parts, not all of which are singletons, of a balanced reduced multisystem. The weight of an atom is 1, while the weight of a multiset is the sum of weights of its elements.
%e A330668 Non-isomorphic representatives of the a(1) = 1 through a(4) = 22 multisystems:
%e A330668 {1} {1,2} {1,2,3} {1,2,3,4}
%e A330668 {{1},{1,2}} {{1},{1,2,3}}
%e A330668 {{1},{2,3}} {{1,2},{1,2}}
%e A330668 {{1,2},{1,3}}
%e A330668 {{1},{2,3,4}}
%e A330668 {{1,2},{3,4}}
%e A330668 {{1},{1},{1,2}}
%e A330668 {{1},{1},{2,3}}
%e A330668 {{1},{2},{1,2}}
%e A330668 {{1},{2},{1,3}}
%e A330668 {{1},{2},{3,4}}
%e A330668 {{{1}},{{1},{1,2}}}
%e A330668 {{{1}},{{1},{2,3}}}
%e A330668 {{{1,2}},{{1},{1}}}
%e A330668 {{{1}},{{2},{1,2}}}
%e A330668 {{{1,2}},{{1},{2}}}
%e A330668 {{{1}},{{2},{1,3}}}
%e A330668 {{{1,2}},{{1},{3}}}
%e A330668 {{{1}},{{2},{3,4}}}
%e A330668 {{{1,2}},{{3},{4}}}
%e A330668 {{{2}},{{1},{1,3}}}
%e A330668 {{{2,3}},{{1},{1}}}
%Y A330668 The case with all atoms different is A318813.
%Y A330668 The version where the leaves are multisets is A330474.
%Y A330668 The tree version is A330626.
%Y A330668 The maximum-depth case is A330677.
%Y A330668 Unlabeled series-reduced rooted trees whose leaves are sets are A330624.
%Y A330668 Cf. A000311, A004114, A005121, A005804, A007716, A048816, A141268, A283877, A306186, A318812, A320154, A330470, A330628, A330663.
%K A330668 nonn,more
%O A330668 0,4
%A A330668 _Gus Wiseman_, Dec 27 2019