A330626 Number of non-isomorphic series/singleton-reduced rooted trees whose leaves are sets (not necessarily disjoint) with a total of n atoms.

1, 1, 1, 3, 17, 100, 755

Offset: 0

Author

Gus Wiseman, Dec 26 2019

Keywords

• nonn
• more

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).

Examples

			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.

Cf. A000669, A004111, A005804, A007716, A141268, A330465, A330625, A330627, A330654, A330663, A330677.