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 A325697 #6 May 17 2019 22:06:25
%S A325697 1,0,1,1,2,2,5,5,11,13,27,30,69,76,168
%N A325697 Number of rooted trees with n vertices with no proper terminal subtree appearing at only one position.
%C A325697 The Matula-Goebel numbers of these trees are given by A325661.
%e A325697 The a(4) = 1 through a(9) = 11 rooted trees:
%e A325697 (ooo) (oooo) (ooooo) (oooooo) (ooooooo) (oooooooo)
%e A325697 ((o)(o)) (o(o)(o)) ((oo)(oo)) (o(oo)(oo)) ((ooo)(ooo))
%e A325697 (oo(o)(o)) (ooo(o)(o)) (oo(oo)(oo))
%e A325697 ((o)(o)(o)) (o(o)(o)(o)) (oooo(o)(o))
%e A325697 (((o))((o))) (o((o))((o))) (oo(o)(o)(o))
%e A325697 (((oo))((oo)))
%e A325697 ((o)(o)(o)(o))
%e A325697 ((o(o))(o(o)))
%e A325697 (oo((o))((o)))
%e A325697 ((o)((o))((o)))
%e A325697 ((((o)))(((o))))
%t A325697 urt[n_]:=Join@@Table[Union[Sort/@Tuples[urt/@ptn]],{ptn,IntegerPartitions[n-1]}];
%t A325697 Table[Length[Select[urt[n],!MemberQ[Length/@Split[Sort[Extract[#,Most[Position[#,_List]]]]],1]&]],{n,15}]
%Y A325697 Cf. A000081, A001694, A004111, A290689, A306844, A317713, A324936, A324971, A325661.
%K A325697 nonn,more
%O A325697 1,5
%A A325697 _Gus Wiseman_, May 17 2019