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%I #6 Sep 12 2018 15:10:28
%S 1,3,25,387,8521,241683,8383705,343826787,16273985641,873119718963,
%T 52360707915385,3470858539699587,252000934472119561,
%U 19888355652445884243,1695252683833578455065,155208762048402360698787,15190477481877333732410281,1582657042668691276257233523
%N Number of phylogenetic plane trees on n labels.
%C 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.
%e The a(2) = 3 phylogenetic plane trees are {1,2}, ({1},{2}), ({2},{1}).
%t sps[{}]:={{}};sps[set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}];
%t t[n_]:=t[n]=1+Sum[Times@@t/@f,{f,Join@@Permutations/@Select[sps[Range[n]],Length[#]>1&]}];
%t Array[t,8]
%Y Cf. A000108, A000670, A001003, A005804, A074206, A118376, A277130, A281118, A281119, A319137.
%K nonn
%O 1,2
%A _Gus Wiseman_, Sep 11 2018
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