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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
OFFSET
0,3
LINKS
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}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 13 2018
STATUS
approved