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%I #8 Apr 27 2020 09:44:02
%S 1,1,3,10,61,410,3630
%N Number of non-isomorphic series-reduced rooted trees whose leaves are sets (not necessarily disjoint) with a total of n elements.
%C A rooted tree is series-reduced if it has no unary branchings, so every non-leaf node covers at least two other nodes.
%e Non-isomorphic representatives of the a(1) = 1 through a(3) = 10 trees:
%e {1} {1,2} {1,2,3}
%e {{1},{1}} {{1},{1,2}}
%e {{1},{2}} {{1},{2,3}}
%e {{1},{1},{1}}
%e {{1},{1},{2}}
%e {{1},{2},{3}}
%e {{1},{{1},{1}}}
%e {{1},{{1},{2}}}
%e {{1},{{2},{3}}}
%e {{2},{{1},{1}}}
%Y The version with multisets as leaves is A330465.
%Y The singleton-reduced case is A330626.
%Y A labeled version is A330625 (strongly normal).
%Y The case with all atoms distinct is A141268.
%Y The case where all leaves are singletons is A330470.
%Y Cf. A000669, A004111, A005804, A007716, A273873, A300660, A320296, A330628, A330668, A330677.
%K nonn,more
%O 0,3
%A _Gus Wiseman_, Dec 25 2019
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