

A319292


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


0




OFFSET

1,3


COMMENTS

A rooted tree is seriesreduced if every nonleaf 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: A231104 A085457 A188911 * A261834 A226740 A244509
Adjacent sequences: A319289 A319290 A319291 * A319293 A319294 A319295


KEYWORD

nonn,more


AUTHOR

Gus Wiseman, Sep 16 2018


STATUS

approved



