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%I #19 Jan 13 2018 13:47:06
%S 1,1,2,5,12,33,91,264,780,2365,7274,22727,71784,229094,737215,2390072,
%T 7798020,25587218,84377881,279499063,929556155,3102767833,10390936382,
%U 34903331506,117564309276,396994228503,1343716120550,4557952756658,15491856887741
%N Number of unlabeled rooted trees with 2n + 1 nodes in which all outdegrees are even.
%H Alois P. Heinz, <a href="/A295461/b295461.txt">Table of n, a(n) for n = 0..1000</a>
%e The a(3) = 5 trees: (o(o(oo))), (o(oooo)), ((oo)(oo)), (ooo(oo)), (oooooo).
%t erut[n_]:=erut[n]=If[n===1,{{}},Join@@Function[c,Union[Sort/@Tuples[erut/@c]]]/@Select[IntegerPartitions[n-1],EvenQ[Length[#]]&]];
%t Table[Length[erut[n]],{n,1,30,2}]
%Y Cf. A000081, A000598, A001190, A003238, A004111, A027193, A027187, A032305, A067659, A290689, A291443, A297791, A298118, A298120, A298126.
%K nonn
%O 0,3
%A _Gus Wiseman_, Jan 13 2018
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