OFFSET
1,2
COMMENTS
A phylogenetic plane tree on n labels is either the set of labels itself or a finite sequence of at least two phylogenetic plane trees, one on each block of an ordered set partition of the labels.
EXAMPLE
The a(2) = 3 phylogenetic plane trees are {1,2}, ({1},{2}), ({2},{1}).
MATHEMATICA
sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];
t[n_]:=t[n]=1+Sum[Times@@t/@f, {f, Join@@Permutations/@Select[sps[Range[n]], Length[#]>1&]}];
Array[t, 8]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 11 2018
STATUS
approved