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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. 25
1, 2, 9, 69, 623, 7793, 110430, 1906317, 36833614, 816101825, 19925210834, 541363267613, 15997458049946, 515769374925576, 17905023985615254, 669030297769291562, 26689471638523499483, 1134895275721374771655, 51161002326406795249910, 2440166138715867838359915 (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
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}]
PROG
(PARI) \\ See A339645 for combinatorial species functions.
cycleIndexSeries(n)={my(v=vector(n)); v[1]=sv(1); for(n=2, #v, v[n] = polcoef( sExp(x*Ser(v[1..n])), n )); x*Ser(v)}
StronglyNormalLabelingsSeq(cycleIndexSeries(15)) \\ Andrew Howroyd, Jan 04 2021
CROSSREFS
Sequence in context: A272663 A006849 A319285 * A330471 A121417 A232549
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 09 2018
EXTENSIONS
Terms a(10) and beyond from Andrew Howroyd, Jan 04 2021
STATUS
approved

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Last modified March 19 01:34 EDT 2024. Contains 370952 sequences. (Running on oeis4.)