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

Author

Gus Wiseman, Jan 13 2018

Keywords

• nonn

Examples

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

Links

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

Crossrefs

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

Programs

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}]