A316501 Number of unlabeled rooted trees with n nodes in which the branches of any node with more than one distinct branch have empty intersection.

1, 1, 2, 4, 9, 19, 45, 103, 250, 611, 1528, 3853, 9875, 25481, 66382, 174085, 459541, 1219462

Offset: 1

Author

Gus Wiseman, Jul 05 2018

Keywords

• nonn
• more

Examples

			The a(6) = 19 rooted trees:
  (((((o)))))
  ((((oo))))
  (((o(o))))
  (((ooo)))
  ((o((o))))
  ((o(oo)))
  (((o)(o)))
  ((oo(o)))
  ((oooo))
  (o(((o))))
  (o((oo)))
  (o(o(o)))
  (o(ooo))
  ((o)((o)))
  (oo((o)))
  (oo(oo))
  (o(o)(o))
  (ooo(o))
  (ooooo)
		

Crossrefs

Cf. A000081, A007562, A289509, A302796, A316470, A316473, A316475, A316500, A316502.

Programs

Mathematica

strut[n_]:=strut[n]=If[n===1,{{}},Select[Join@@Function[c,Union[Sort/@Tuples[strut/@c]]]/@IntegerPartitions[n-1],Or[Length[Union[#]]==1,Intersection@@#=={}]&]];
Table[Length[strut[n]],{n,15}]