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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. 36
 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 Andrew Howroyd, Table of n, a(n) for n = 1..200 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 Cf. A000081, A000311, A000669, A001678, A005804, A141268, A292504, A300660, A316653, A316654, A316656. Sequence in context: A242566 A148686 A148687 * A325213 A148688 A259809 Adjacent sequences:  A319309 A319310 A319311 * A319313 A319314 A319315 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 April 6 16:14 EDT 2020. Contains 333276 sequences. (Running on oeis4.)