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%I #5 Jul 05 2018 07:21:21
%S 1,1,1,2,3,6,11,22,46,96,205,442,976,2146,4789,10719,24202,54841,
%T 124967,285724,656011,1510929,3491151,8088692,18790084
%N Number of unlabeled rooted identity trees with n nodes in which the branches of any node with more than one branch have empty intersection.
%e The a(7) = 11 rooted identity trees:
%e ((((((o))))))
%e ((((o(o)))))
%e (((o((o)))))
%e ((o(((o)))))
%e ((o(o(o))))
%e (((o)((o))))
%e (o((((o)))))
%e (o((o(o))))
%e (o(o((o))))
%e ((o)(((o))))
%e (o(o)((o)))
%t strut[n_]:=strut[n]=If[n===1,{{}},Select[Join@@Function[c,Union[Sort/@Tuples[strut/@c]]]/@IntegerPartitions[n-1],UnsameQ@@#&&Or[Length[#]==1,Intersection@@#=={}]&]];
%t Table[Length[strut[n]],{n,20}]
%Y Cf. A000081, A004111, A007562, A078374, A289509, A316469, A316471, A316474, A316501, A316503.
%K nonn,more
%O 1,4
%A _Gus Wiseman_, Jul 05 2018
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