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A295461 Number of unlabeled rooted trees with 2n + 1 nodes in which all outdegrees are even. 9
1, 1, 2, 5, 12, 33, 91, 264, 780, 2365, 7274, 22727, 71784, 229094, 737215, 2390072, 7798020, 25587218, 84377881, 279499063, 929556155, 3102767833, 10390936382, 34903331506, 117564309276, 396994228503, 1343716120550, 4557952756658, 15491856887741 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

EXAMPLE

The a(3) = 5 trees: (o(o(oo))), (o(oooo)), ((oo)(oo)), (ooo(oo)), (oooooo).

MATHEMATICA

erut[n_]:=erut[n]=If[n===1, {{}}, Join@@Function[c, Union[Sort/@Tuples[erut/@c]]]/@Select[IntegerPartitions[n-1], EvenQ[Length[#]]&]];

Table[Length[erut[n]], {n, 1, 30, 2}]

CROSSREFS

Cf. A000081, A000598, A001190, A003238, A004111, A027193, A027187, A032305, A067659, A290689, A291443, A297791, A298118, A298120, A298126.

Sequence in context: A292215 A292216 A000669 * A191769 A221206 A281489

Adjacent sequences:  A295458 A295459 A295460 * A295462 A295463 A295464

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jan 13 2018

STATUS

approved

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Last modified December 2 10:53 EST 2021. Contains 349440 sequences. (Running on oeis4.)