OFFSET
1,3
COMMENTS
A strict tree of weight n > 0 is either a single node of weight n, or a sequence of two or more strict trees with strictly decreasing weights summing to n.
EXAMPLE
The a(8) = 11 strict trees with distinct leaves: 8, (71), ((52)1), ((43)1), (62), ((51)2), (53), ((41)3), (5(21)), (521), (431).
MATHEMATICA
sps[{}]:={{}}; sps[set:{i_, ___}]:=
Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];
str[q_]:=str[q]=If[Length[q]===1, 1, Total[Times@@@Map[str, Select[sps[q], And[Length[#]>1, UnsameQ@@Total/@#]&], {2}]]];
Table[Total[str/@Select[IntegerPartitions[n], UnsameQ@@#&]], {n, 1, 20}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 03 2018
STATUS
approved