cp's OEIS Frontend

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.

%I A316501 #5 Jul 05 2018 07:21:29
%S A316501 1,1,2,4,9,19,45,103,250,611,1528,3853,9875,25481,66382,174085,459541,
%T A316501 1219462
%N 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.
%e A316501 The a(6) = 19 rooted trees:
%e A316501   (((((o)))))
%e A316501   ((((oo))))
%e A316501   (((o(o))))
%e A316501   (((ooo)))
%e A316501   ((o((o))))
%e A316501   ((o(oo)))
%e A316501   (((o)(o)))
%e A316501   ((oo(o)))
%e A316501   ((oooo))
%e A316501   (o(((o))))
%e A316501   (o((oo)))
%e A316501   (o(o(o)))
%e A316501   (o(ooo))
%e A316501   ((o)((o)))
%e A316501   (oo((o)))
%e A316501   (oo(oo))
%e A316501   (o(o)(o))
%e A316501   (ooo(o))
%e A316501   (ooooo)
%t A316501 strut[n_]:=strut[n]=If[n===1,{{}},Select[Join@@Function[c,Union[Sort/@Tuples[strut/@c]]]/@IntegerPartitions[n-1],Or[Length[Union[#]]==1,Intersection@@#=={}]&]];
%t A316501 Table[Length[strut[n]],{n,15}]
%Y A316501 Cf. A000081, A007562, A289509, A302796, A316470, A316473, A316475, A316500, A316502.
%K A316501 nonn,more
%O A316501 1,3
%A A316501 _Gus Wiseman_, Jul 05 2018