A330624 Number of non-isomorphic series-reduced rooted trees whose leaves are sets (not necessarily disjoint) with a total of n elements.

1, 1, 3, 10, 61, 410, 3630

Offset: 0

Author

Gus Wiseman, Dec 25 2019

Keywords

• nonn
• more

Comments

A rooted tree is series-reduced if it has no unary branchings, so every non-leaf node covers at least two other nodes.

Examples

			Non-isomorphic representatives of the a(1) = 1 through a(3) = 10 trees:
  {1}  {1,2}      {1,2,3}
       {{1},{1}}  {{1},{1,2}}
       {{1},{2}}  {{1},{2,3}}
                  {{1},{1},{1}}
                  {{1},{1},{2}}
                  {{1},{2},{3}}
                  {{1},{{1},{1}}}
                  {{1},{{1},{2}}}
                  {{1},{{2},{3}}}
                  {{2},{{1},{1}}}
		

Crossrefs

The version with multisets as leaves is A330465.

The singleton-reduced case is A330626.

A labeled version is A330625 (strongly normal).

The case with all atoms distinct is A141268.

The case where all leaves are singletons is A330470.

Cf. A000669, A004111, A005804, A007716, A273873, A300660, A320296, A330628, A330668, A330677.