This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A316500 #5 Jul 05 2018 07:21:21
%S A316500 1,1,1,2,3,6,11,22,46,96,205,442,976,2146,4789,10719,24202,54841,
%T A316500 124967,285724,656011,1510929,3491151,8088692,18790084
%N A316500 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 A316500 The a(7) = 11 rooted identity trees:
%e A316500 ((((((o))))))
%e A316500 ((((o(o)))))
%e A316500 (((o((o)))))
%e A316500 ((o(((o)))))
%e A316500 ((o(o(o))))
%e A316500 (((o)((o))))
%e A316500 (o((((o)))))
%e A316500 (o((o(o))))
%e A316500 (o(o((o))))
%e A316500 ((o)(((o))))
%e A316500 (o(o)((o)))
%t A316500 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 A316500 Table[Length[strut[n]],{n,20}]
%Y A316500 Cf. A000081, A004111, A007562, A078374, A289509, A316469, A316471, A316474, A316501, A316503.
%K A316500 nonn,more
%O A316500 1,4
%A A316500 _Gus Wiseman_, Jul 05 2018