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A316652 Number of series-reduced rooted trees whose leaves span an initial interval of positive integers with multiplicities an integer partition of n. 24
1, 2, 9, 69, 623, 7793, 110430, 1906317, 36833614 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A rooted tree is series-reduced if every non-leaf node has at least two branches.

LINKS

Table of n, a(n) for n=1..9.

EXAMPLE

The a(3) = 9 trees:

(1(11)), (111),

(1(12)), (2(11)), (112),

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

Table[Sum[Length[gro[m]], {m, Flatten[MapIndexed[Table[#2, {#1}]&, #]]&/@IntegerPartitions[n]}], {n, 4}]

CROSSREFS

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

Cf. A316651, A316653, A316654, A316655, A316656.

Sequence in context: A272663 A006849 A319285 * A330471 A121417 A232549

Adjacent sequences:  A316649 A316650 A316651 * A316653 A316654 A316655

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Jul 09 2018

STATUS

approved

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Last modified February 18 15:30 EST 2020. Contains 332019 sequences. (Running on oeis4.)