OFFSET
0,4
COMMENTS
An enriched p-tree of weight n > 0 is either a single node of weight n, or a sequence of two or more enriched p-trees with weakly decreasing weights summing to n.
EXAMPLE
The a(6) = 8 enriched p-trees with distinct leaves: 6, (42), (51), ((31)2), ((32)1), (3(21)), ((21)3), (321).
MATHEMATICA
sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];
ept[q_]:=ept[q]=If[Length[q]===1, 1, Total[Times@@@Map[ept, Join@@Function[sptn, Join@@@Tuples[Permutations/@GatherBy[sptn, Total]]]/@Select[sps[q], Length[#]>1&], {2}]]];
Table[Total[ept/@Select[IntegerPartitions[n], UnsameQ@@#&]], {n, 1, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 03 2018
STATUS
approved