# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a324839 Showing 1-1 of 1 %I A324839 #4 Mar 19 2019 07:14:41 %S A324839 1,0,1,1,2,3,8,16,35,74,166,367,831,1878,4299,9857,22775,52777,122957, %T A324839 287337 %N A324839 Number of unlabeled rooted identity trees with n nodes where the branches of no branch of the root form a subset of the branches of the root. %C A324839 An unlabeled rooted tree is an identity tree if there are no repeated branches directly under the same root. %C A324839 Also the number of finitary sets with n brackets where no element is also a subset. For example, the a(7) = 8 sets are (o = {}): %C A324839 {{{{{{o}}}}}} %C A324839 {{{{o,{o}}}}} %C A324839 {{{o,{{o}}}}} %C A324839 {{o,{{{o}}}}} %C A324839 {{o,{o,{o}}}} %C A324839 {{{o},{{o}}}} %C A324839 {{o},{{{o}}}} %C A324839 {{o},{o,{o}}} %e A324839 The a(1) = 1 through a(8) = 16 rooted identity trees: %e A324839 o ((o)) (((o))) ((o(o))) (((o(o)))) ((o)(o(o))) (((o))(o(o))) %e A324839 ((((o)))) ((o((o)))) ((o(o(o)))) (((o)(o(o)))) %e A324839 (((((o))))) ((((o(o))))) (((o(o(o))))) %e A324839 (((o)((o)))) ((o)((o(o)))) %e A324839 (((o((o))))) ((o)(o((o)))) %e A324839 ((o)(((o)))) ((o((o(o))))) %e A324839 ((o(((o))))) ((o(o)((o)))) %e A324839 ((((((o)))))) ((o(o((o))))) %e A324839 (((((o(o)))))) %e A324839 ((((o)((o))))) %e A324839 ((((o((o)))))) %e A324839 (((o)(((o))))) %e A324839 (((o(((o)))))) %e A324839 ((o)((((o))))) %e A324839 ((o((((o)))))) %e A324839 (((((((o))))))) %t A324839 idall[n_]:=If[n==1,{{}},Select[Union[Sort/@Join@@(Tuples[idall/@#]&/@IntegerPartitions[n-1])],UnsameQ@@#&]]; %t A324839 Table[Length[Select[idall[n],And@@Table[!SubsetQ[#,b],{b,#}]&]],{n,10}] %Y A324839 Cf. A000081, A290760, A304360, A306844, A317787. %Y A324839 Cf. A324694, A324696, A324704, A324738, A324744, A324758, A324759, A324767, A324770, A324771, A324838, A324840, A324844, A324846. %K A324839 nonn,more %O A324839 1,5 %A A324839 _Gus Wiseman_, Mar 18 2019 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE