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 A306844 #14 Jun 20 2020 02:04:43
%S A306844 1,1,2,3,7,14,36,83,212,532,1379,3577,9444,25019,66943,179994,487031,
%T A306844 1323706,3614622,9907911
%N A306844 Number of anti-transitive rooted trees with n nodes.
%C A306844 A rooted tree is anti-transitive if the subbranches are disjoint from the branches, i.e., no branch of a branch is a branch.
%H A306844 Gus Wiseman, <a href="/A306844/a306844.png">The a(7) = 36 anti-transitive rooted trees</a>.
%H A306844 Gus Wiseman, <a href="/A306844/a306844_1.png">The a(10) = 532 anti-transitive rooted trees</a>.
%e A306844 The a(1) = 1 through a(6) = 14 anti-transitive rooted trees:
%e A306844 o (o) (oo) (ooo) (oooo) (ooooo)
%e A306844 ((o)) ((oo)) ((ooo)) ((oooo))
%e A306844 (((o))) (((oo))) (((ooo)))
%e A306844 ((o)(o)) ((o)(oo))
%e A306844 ((o(o))) ((o(oo)))
%e A306844 (o((o))) ((oo(o)))
%e A306844 ((((o)))) (o((oo)))
%e A306844 (oo((o)))
%e A306844 ((((oo))))
%e A306844 (((o)(o)))
%e A306844 (((o(o))))
%e A306844 ((o((o))))
%e A306844 (o(((o))))
%e A306844 (((((o)))))
%t A306844 rtall[n_]:=Union[Sort/@Join@@(Tuples[rtall/@#]&/@IntegerPartitions[n-1])];
%t A306844 Table[Length[Select[rtall[n],Intersection[Union@@#,#]=={}&]],{n,10}]
%Y A306844 Cf. A276625, A279861, A279861, A290689, A290760, A304360.
%Y A306844 Cf. A324694, A324695, A324738, A324741, A324743, A324751, A324754, A324756, A324758, A324759, A324764.
%K A306844 nonn,more
%O A306844 1,3
%A A306844 _Gus Wiseman_, Mar 13 2019
%E A306844 a(16)-a(20) from _Jinyuan Wang_, Jun 20 2020