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 A298422 Number of rooted trees with n nodes in which all positive outdegrees are the same. 44
 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, 2182, 215, 4902, 2, 11446, 2, 24744, 1242, 56014, 58, 131258, 2, 293550, 7643, 676928, 2, 1582686, 2, 3627780, 49155, 8436382, 2, 19809464, 50, 46027323, 321202 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Row sums of A298426. LINKS Alois P. Heinz, Table of n, a(n) for n = 1..200 FORMULA a(n) = 2 <=> n in {A008864}. - Alois P. Heinz, Jan 20 2018 EXAMPLE The a(9) = 6 trees: ((((((((o)))))))), (o(o(o(oo)))), (o((oo)(oo))), ((oo)(o(oo))), (ooo(oooo)), (oooooooo). MATHEMATICA 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}]&]]; Table[srut[n]//Length, {n, 20}] CROSSREFS Cf. A000005, A000081, A000598, A001190, A001678, A003238, A004111, A008864, A032305, A067538, A111299, A124343, A143773, A289078, A289079, A295461, A298118, A298204, A298423, A298424, A298426. Sequence in context: A115119 A066656 A164896 * A304716 A237984 A118136 Adjacent sequences:  A298419 A298420 A298421 * A298423 A298424 A298425 KEYWORD nonn AUTHOR Gus Wiseman, Jan 19 2018 EXTENSIONS a(44)-a(52) from Alois P. Heinz, Jan 20 2018 STATUS approved

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Last modified April 11 06:11 EDT 2021. Contains 342886 sequences. (Running on oeis4.)