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A316654 Number of series-reduced rooted identity trees whose leaves span an initial interval of positive integers with multiplicities an integer partition of n. 9
1, 1, 5, 39, 387, 4960, 74088, 1312716 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

A rooted tree is series-reduced if every non-leaf node has at least two branches. It is an identity tree if no branch appears multiple times under the same root.

LINKS

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

EXAMPLE

The a(3) = 5 trees are (1(12)), (1(23)), (2(13)), (3(12)), (123).

MATHEMATICA

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_]:=If[Length[m]==1, m, Select[Union[Sort/@Join@@(Tuples[gro/@#]&/@Select[mps[m], Length[#]>1&])], UnsameQ@@#&]];

Table[Sum[Length[gro[m]], {m, Flatten[MapIndexed[Table[#2, {#1}]&, #]]&/@IntegerPartitions[n]}], {n, 5}]

CROSSREFS

Cf. A000081, A000311, A000669, A001678, A004111, A005804, A141268, A181821, A292504, A300660, A304660.

Cf. A316651, A316652, A316653, A316655, A316656.

Sequence in context: A277424 A182954 A215506 * A070767 A124549 A308939

Adjacent sequences:  A316651 A316652 A316653 * A316655 A316656 A316657

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Jul 09 2018

STATUS

approved

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Last modified April 4 05:34 EDT 2020. Contains 333212 sequences. (Running on oeis4.)