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%I #10 Sep 17 2018 03:16:52
%S 1,1,2,4,8,18,40,95,227,557,1382,3485,8865,22790,59022,153972,404066,
%T 1066236,2826885,7527411,20121154
%N Number of locally nonintersecting rooted trees with n nodes.
%C An unlabeled rooted tree is locally nonintersecting if there is no common subbranch to all branches directly under any given node.
%e The a(6) = 18 locally nonintersecting rooted trees:
%e (((((o)))))
%e ((((oo))))
%e (((o(o))))
%e ((o((o))))
%e (o(((o))))
%e ((o)((o)))
%e (((ooo)))
%e ((o(oo)))
%e ((oo(o)))
%e (o((oo)))
%e (o(o(o)))
%e (oo((o)))
%e (o(o)(o))
%e ((oooo))
%e (o(ooo))
%e (oo(oo))
%e (ooo(o))
%e (ooooo)
%e Missing from this list are (((o)(o))) and ((o)(oo)).
%t rurt[n_]:=If[n==1,{{}},Join@@Table[Select[Union[Sort/@Tuples[rurt/@ptn]],Or[Length[#]==1,Intersection@@#=={}]&],{ptn,IntegerPartitions[n-1]}]];
%t Table[Length[rurt[n]],{n,10}]
%Y Cf. A000081, A276625, A301700, A316473, A316475, A316501, A316502, A317708, A317785, A317789.
%K nonn,more
%O 1,3
%A _Gus Wiseman_, Aug 07 2018
%E a(16)-a(21) from _Robert Price_, Sep 16 2018
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