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 A298118 Number of unlabeled rooted trees with n nodes in which all positive outdegrees are odd. 27
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..1000 FORMULA a(n) ~ c * d^n / n^(3/2), where d = 2.30984417428419893876754252289588812511559... and c = 0.5598122522173731208680575003383895445787... - Vaclav Kotesovec, Jun 04 2019 EXAMPLE The a(6) = 6 trees: (((((o))))), (((ooo))), ((oo(o))), (oo((o))), (o(o)(o)), (ooooo). MATHEMATICA 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}] CROSSREFS Cf. A000081, A000598, A003238, A004111, A027193, A032305, A067659, A290689, A291443, A297791, A298120. Sequence in context: A306575 A006861 A052956 * A008930 A164362 A026742 Adjacent sequences:  A298115 A298116 A298117 * A298119 A298120 A298121 KEYWORD nonn AUTHOR Gus Wiseman, Jan 12 2018 EXTENSIONS a(24)-a(35) from Alois P. Heinz, Jan 12 2018 STATUS approved

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Last modified October 14 17:31 EDT 2019. Contains 328022 sequences. (Running on oeis4.)