A319292 Number of series-reduced locally nonintersecting rooted trees whose leaves span an initial interval of positive integers with multiplicities an integer partition of n.

1, 1, 6, 48, 455, 5700, 83138, 1454870

Offset

1,3

Comments

A rooted tree is series-reduced if every non-leaf node has at least two branches. It is locally nonintersecting if the intersection of all branches directly under any given node with at least two branches is empty.

Links

Table of n, a(n) for n=1..8.

Example

The a(3) = 6 trees are: (1(12)), (112), (1(23)), (2(13)), (3(12)), (123). Missing from this list but counted by A316651 are: (1(11)), (2(11)), (111).

Mathematica

nonintQ[u_]:=Intersection@@u=={};
sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];
mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]];
gro[m_]:=gro[m]=If[Length[m]==1, {m}, Select[Union[Sort/@Join@@(Tuples[gro/@#]&/@Select[mps[m], Length[#]>1&])], nonintQ]];
Table[Sum[Length[gro[m]], {m, Flatten[MapIndexed[Table[#2, {#1}]&, #]]&/@IntegerPartitions[n]}], {n, 5}]

Crossrefs

Cf. A000081, A007562, A273873, A289509, A301700, A316470, A316473, A316475, A316651, A319271.

Sequence in context: A364923 A365192 A365187 * A261834 A226740 A244509

Adjacent sequences: A319289 A319290 A319291 * A319293 A319294 A319295

Keyword

nonn,more

Author

Gus Wiseman, Sep 16 2018

Status

approved