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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

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: A191789 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 February 16 21:59 EST 2019. Contains 320200 sequences. (Running on oeis4.)