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A319312 Number of series-reduced rooted trees whose leaves are integer partitions whose multiset union is an integer partition of n. 37
1, 3, 7, 22, 67, 242, 885, 3456, 13761, 56342, 234269, 989335, 4225341, 18231145, 79321931, 347676128, 1533613723, 6803017863, 30328303589, 135808891308, 610582497919, 2755053631909, 12472134557093, 56630659451541, 257841726747551, 1176927093597201 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Also the number of orderless tree-factorizations of Heinz numbers of integer partitions of n.
Also the number of phylogenetic trees on a multiset of labels summing to n.
LINKS
EXAMPLE
The a(3) = 7 trees:
(3) (21) (111)
((1)(2)) ((1)(11))
((1)(1)(1))
((1)((1)(1)))
MATHEMATICA
facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]];
phyfacs[n_]:=Prepend[Join@@Table[Union[Sort/@Tuples[phyfacs/@f]], {f, Select[facs[n], Length[#]>1&]}], n];
Table[Sum[Length[phyfacs[Times@@Prime/@m]], {m, IntegerPartitions[n]}], {n, 6}]
PROG
(PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
seq(n)={my(v=[]); for(n=1, n, v=concat(v, numbpart(n) + EulerT(concat(v, [0]))[n])); v} \\ Andrew Howroyd, Sep 18 2018
CROSSREFS
Sequence in context: A242566 A148686 A148687 * A325213 A148688 A045610
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 17 2018
EXTENSIONS
Terms a(14) and beyond from Andrew Howroyd, Sep 18 2018
STATUS
approved

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