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%I #11 Jun 20 2020 03:20:28
%S 1,1,2,4,9,19,44,99,233,554,1346,3300,8219,20635,52300,133488,343033,
%T 886360,2302133,6005835
%N Number of locally disjoint rooted trees with n nodes, meaning no branch overlaps any other (unequal) branch of the same root.
%H Gus Wiseman, <a href="/A316473/a316473.png">The a(6) = 19 locally disjoint rooted trees.</a>
%e The a(5) = 9 locally disjoint rooted trees:
%e ((((o))))
%e (((oo)))
%e ((o(o)))
%e ((ooo))
%e (o((o)))
%e (o(oo))
%e ((o)(o))
%e (oo(o))
%e (oooo)
%t strut[n_]:=strut[n]=If[n===1,{{}},Select[Join@@Function[c,Union[Sort/@Tuples[strut/@c]]]/@IntegerPartitions[n-1],Select[Tuples[#,2],UnsameQ@@#&&(Intersection@@#=!={})&]=={}&]];
%t Table[Length[strut[n]],{n,15}]
%Y Cf. A000081, A285573, A302696, A304713, A316468, A316470, A316471, A316475, A316495.
%K nonn,more
%O 1,3
%A _Gus Wiseman_, Jul 04 2018
%E a(20) from _Jinyuan Wang_, Jun 20 2020
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