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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 17 2018
EXTENSIONS
Terms a(14) and beyond from Andrew Howroyd, Sep 18 2018
STATUS
approved