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%I #12 Jan 20 2018 12:03:12
%S 1,1,2,2,3,2,5,2,6,4,9,2,20,2,26,12,53,2,120,2,223,43,454,2,1100,11,
%T 2182,215,4902,2,11446,2,24744,1242,56014,58,131258,2,293550,7643,
%U 676928,2,1582686,2,3627780,49155,8436382,2,19809464,50,46027323,321202
%N Number of rooted trees with n nodes in which all positive outdegrees are the same.
%C Row sums of A298426.
%H Alois P. Heinz, <a href="/A298422/b298422.txt">Table of n, a(n) for n = 1..200</a>
%F a(n) = 2 <=> n in {A008864}. - _Alois P. Heinz_, Jan 20 2018
%e The a(9) = 6 trees: ((((((((o)))))))), (o(o(o(oo)))), (o((oo)(oo))), ((oo)(o(oo))), (ooo(oooo)), (oooooooo).
%t srut[n_]:=srut[n]=If[n===1,{{}},Select[Join@@Function[c,Union[Sort/@Tuples[srut/@c]]]/@Select[IntegerPartitions[n-1],Function[ptn,And@@(Divisible[#-1,Length[ptn]]&/@ptn)]],SameQ@@Length/@Cases[#,{__},{0,Infinity}]&]];
%t Table[srut[n]//Length,{n,20}]
%Y Cf. A000005, A000081, A000598, A001190, A001678, A003238, A004111, A008864, A032305, A067538, A111299, A124343, A143773, A289078, A289079, A295461, A298118, A298204, A298423, A298424, A298426.
%K nonn
%O 1,3
%A _Gus Wiseman_, Jan 19 2018
%E a(44)-a(52) from _Alois P. Heinz_, Jan 20 2018
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