A319122 Number of phylogenetic plane trees on n labels.

1, 3, 25, 387, 8521, 241683, 8383705, 343826787, 16273985641, 873119718963, 52360707915385, 3470858539699587, 252000934472119561, 19888355652445884243, 1695252683833578455065, 155208762048402360698787, 15190477481877333732410281, 1582657042668691276257233523

Offset: 1

Author

Gus Wiseman, Sep 11 2018

Keywords

• nonn

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.

Examples

			The a(2) = 3 phylogenetic plane trees are {1,2}, ({1},{2}), ({2},{1}).
		

Crossrefs

Cf. A000108, A000670, A001003, A005804, A074206, A118376, A277130, A281118, A281119, A319137.

Programs

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]