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A298118
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Number of unlabeled rooted trees with n nodes in which all positive outdegrees are odd.
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28
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1, 1, 1, 2, 3, 6, 11, 21, 40, 80, 159, 322, 657, 1356, 2816, 5896, 12407, 26267, 55861, 119331, 255878, 550665, 1188786, 2574006, 5588177, 12162141, 26529873, 57993624, 127020653, 278716336, 612617523, 1348680531, 2973564157, 6565313455, 14514675376
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OFFSET
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1,4
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LINKS
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FORMULA
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a(n) ~ c * d^n / n^(3/2), where d = 2.30984417428419893876754252289588812511559... and c = 0.5598122522173731208680575003383895445787... - Vaclav Kotesovec, Jun 04 2019
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EXAMPLE
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The a(6) = 6 trees: (((((o))))), (((ooo))), ((oo(o))), (oo((o))), (o(o)(o)), (ooooo).
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MATHEMATICA
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orut[n_]:=orut[n]=If[n===1, {{}}, Join@@Function[c, Union[Sort/@Tuples[orut/@c]]]/@Select[IntegerPartitions[n-1], OddQ[Length[#]]&]];
Table[Length[orut[n]], {n, 15}]
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CROSSREFS
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Cf. A000081, A000598, A003238, A004111, A027193, A032305, A067659, A290689, A291443, A297791, A298120.
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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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