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A330626 Number of non-isomorphic series/singleton-reduced rooted trees whose leaves are sets (not necessarily disjoint) with a total of n atoms. 8
1, 1, 1, 3, 17, 100, 755 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
A series/singleton-reduced rooted tree on a multiset m is either the multiset m itself or a sequence of series/singleton-reduced rooted trees, one on each part of a multiset partition of m that is neither minimal (all singletons) nor maximal (only one part).
LINKS
EXAMPLE
Non-isomorphic representatives of the a(1) = 1 through a(4) = 17 trees:
{1} {1,2} {1,2,3} {1,2,3,4}
{{1},{1,2}} {{1},{1,2,3}}
{{1},{2,3}} {{1,2},{1,2}}
{{1,2},{1,3}}
{{1},{2,3,4}}
{{1,2},{3,4}}
{{1},{1},{1,2}}
{{1},{1},{2,3}}
{{1},{2},{1,2}}
{{1},{2},{1,3}}
{{1},{2},{3,4}}
{{1},{{1},{1,2}}}
{{1},{{1},{2,3}}}
{{1},{{2},{1,2}}}
{{1},{{2},{1,3}}}
{{1},{{2},{3,4}}}
{{2},{{1},{1,3}}}
CROSSREFS
The non-singleton-reduced version is A330624.
The generalization where leaves are multisets is A330470.
A labeled version is A330628 (strongly normal).
The case with all atoms distinct is A004114.
The balanced version is A330668.
Sequence in context: A001541 A322242 A356392 * A161940 A074565 A339565
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Dec 26 2019
STATUS
approved

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Last modified April 14 09:38 EDT 2024. Contains 371657 sequences. (Running on oeis4.)