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

0,3

Comments

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

Links

Table of n, a(n) for n=0..6.

Example

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.

Sequence in context: A009654 A013565 A156075 * A228773 A034889 A260969

Adjacent sequences: A330621 A330622 A330623 * A330625 A330626 A330627

Keyword

nonn,more

Author

Gus Wiseman, Dec 25 2019

Status

approved