%I
%S 1,0,1,1,1,1,2,1,2,2,2,1,5,1,3,3,4,3,5,3,6,4,6,3,12,3,10,7,9,6,12,9,
%T 13,16,14,22,22,24,21,24,28,14,32,15,42,20,60,27,84,44,100,59,113,74,
%U 116,85,110,97,96,113,106,149,147,234,235,377,380,580,576,838
%N Number of seriesreduced leafbalanced rooted trees with n nodes. Number of orderless sametrees with n nodes and all leaves equal to 1.
%C An unlabeled rooted tree is leafbalanced if all branches from the same root have the same number of leaves. It is seriesreduced if all positive outdegrees are greater than one.
%H Robert G. Wilson v, <a href="/A297791/b297791.txt">Table of n, a(n) for n = 1..84</a>
%e The a(13) = 5 trees: (((oo)(oo))(oooo)), ((ooooo)(ooooo)), ((ooo)(ooo)(ooo)), ((oo)(oo)(oo)(oo)), (oooooooooooo).
%t alltim[n_]:=alltim[n]=If[n===1,{{}},Join@@Function[c,Select[Union[Sort/@Tuples[alltim/@c]],And[SameQ@@(Count[#,{},{0,Infinity}]&/@#),FreeQ[#,{_}]]&]]/@IntegerPartitions[n1]];
%t Table[Length[alltim[n]],{n,20}]
%Y Cf. A000081, A001190, A001678, A006241, A032305, A289078, A289079, A291441, A291443.
%K nonn,more
%O 1,7
%A _Gus Wiseman_, Jan 06 2018
%E a(51) onward from _Robert G. Wilson v_, Jan 07 2018
