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A319122
Number of phylogenetic plane trees on n labels.
11
1, 3, 25, 387, 8521, 241683, 8383705, 343826787, 16273985641, 873119718963, 52360707915385, 3470858539699587, 252000934472119561, 19888355652445884243, 1695252683833578455065, 155208762048402360698787, 15190477481877333732410281, 1582657042668691276257233523
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]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 11 2018
STATUS
approved