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%I #14 Jun 20 2020 02:04:43
%S 1,1,2,3,7,14,36,83,212,532,1379,3577,9444,25019,66943,179994,487031,
%T 1323706,3614622,9907911
%N Number of anti-transitive rooted trees with n nodes.
%C 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 Gus Wiseman, <a href="/A306844/a306844.png">The a(7) = 36 anti-transitive rooted trees</a>.
%H Gus Wiseman, <a href="/A306844/a306844_1.png">The a(10) = 532 anti-transitive rooted trees</a>.
%e The a(1) = 1 through a(6) = 14 anti-transitive rooted trees:
%e o (o) (oo) (ooo) (oooo) (ooooo)
%e ((o)) ((oo)) ((ooo)) ((oooo))
%e (((o))) (((oo))) (((ooo)))
%e ((o)(o)) ((o)(oo))
%e ((o(o))) ((o(oo)))
%e (o((o))) ((oo(o)))
%e ((((o)))) (o((oo)))
%e (oo((o)))
%e ((((oo))))
%e (((o)(o)))
%e (((o(o))))
%e ((o((o))))
%e (o(((o))))
%e (((((o)))))
%t rtall[n_]:=Union[Sort/@Join@@(Tuples[rtall/@#]&/@IntegerPartitions[n-1])];
%t Table[Length[Select[rtall[n],Intersection[Union@@#,#]=={}&]],{n,10}]
%Y Cf. A276625, A279861, A279861, A290689, A290760, A304360.
%Y Cf. A324694, A324695, A324738, A324741, A324743, A324751, A324754, A324756, A324758, A324759, A324764.
%K nonn,more
%O 1,3
%A _Gus Wiseman_, Mar 13 2019
%E a(16)-a(20) from _Jinyuan Wang_, Jun 20 2020
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