A295461 Number of unlabeled rooted trees with 2n + 1 nodes in which all outdegrees are even.

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

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