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%I #16 Dec 26 2014 14:55:48
%S 1,1,1,2,4,10,24,58,142,359,919,2384,6240,16487,43894,117689,317400,
%T 860585,2344280,6413109,17610746,48527584,134141036,371862499,
%U 1033586232,2879818131,8041864259,22503532974,63093269641,177213423131
%N a(n) = number of unlabeled rooted trees on n nodes with an odd number of endpoints.
%H F. Harary and E. M. Palmer, <a href="http://users.aims.ac.za/~stephan/GraphicalEnumeration.pdf">Graphical Enumeration</a>, Academic Press, NY, 1973; see pp. 51-55.
%H Marko Riedel, <a href="http://math.stackexchange.com/questions/1080099/">Unlabled rooted trees with even and odd numbers of endpoints</a>
%p T :=
%p proc(n)
%p option remember;
%p local k, s, A;
%p if n=0 then return 0 fi;
%p if n=1 then return u fi;
%p A := n -> add(subs(u=u^l, T(n/l))/l,
%p l in divisors(n));
%p s := (1-u)*A(n-1);
%p s := s + 1/(n-1)*
%p add((k+1)*A(k+1)*T(n-1-k), k=0..n-2);
%p expand(s);
%p end;
%Y Cf. A000081, A253013.
%K nonn
%O 1,4
%A _Marko Riedel_, Dec 25 2014
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