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 A324770 #4 Mar 18 2019 08:15:46
%S A324770 1,1,1,1,2,3,6,13,27,58,128,286,640,1452,3308,7594,17512,40591,94449,
%T A324770 220672
%N A324770 Number of fully anti-transitive rooted identity trees with n nodes.
%C A324770 An unlabeled rooted tree is fully anti-transitive if no proper terminal subtree of any branch of the root is a branch of the root. It is an identity tree if there are no repeated branches directly under the same root.
%H A324770 Gus Wiseman, <a href="/A324770/a324770.png">The a(11) = 128 fully anti-transitive rooted identity trees</a>.
%e A324770 The a(1) = 1 through a(7) = 6 fully anti-transitive rooted identity trees:
%e A324770 o (o) ((o)) (((o))) ((o(o))) (((o(o)))) ((o(o(o))))
%e A324770 ((((o)))) ((o((o)))) ((((o(o)))))
%e A324770 (((((o))))) (((o)((o))))
%e A324770 (((o((o)))))
%e A324770 ((o(((o)))))
%e A324770 ((((((o))))))
%t A324770 idall[n_]:=If[n==1,{{}},Select[Union[Sort/@Join@@(Tuples[idall/@#]&/@IntegerPartitions[n-1])],UnsameQ@@#&]];
%t A324770 Table[Length[Select[idall[n],Intersection[Union@@Rest[FixedPointList[Union@@#&,#]],#]=={}&]],{n,10}]
%Y A324770 Cf. A000081, A004111, A276625, A279861, A290760, A304360, A306844.
%Y A324770 Cf. A324695, A324751, A324763, A324764, A324765, A324767, A324769.
%Y A324770 Cf. A324839, A324840, A324843, A324844, A324846.
%K A324770 nonn,more
%O A324770 1,5
%A A324770 _Gus Wiseman_, Mar 17 2019