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A298422
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Number of rooted trees with n nodes in which all positive outdegrees are the same.
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44
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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
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OFFSET
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1,3
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COMMENTS
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LINKS
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FORMULA
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EXAMPLE
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The a(9) = 6 trees: ((((((((o)))))))), (o(o(o(oo)))), (o((oo)(oo))), ((oo)(o(oo))), (ooo(oooo)), (oooooooo).
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MATHEMATICA
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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}]
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CROSSREFS
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Cf. A000005, A000081, A000598, A001190, A001678, A003238, A004111, A008864, A032305, A067538, A111299, A124343, A143773, A289078, A289079, A295461, A298118, A298204, A298423, A298424, A298426.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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