cp's OEIS Frontend

A253013 a(n) = number of unlabeled rooted trees on n nodes with an even number of endpoints.

%I A253013 #20 Dec 26 2014 14:55:08
%S A253013 0,0,1,2,5,10,24,57,144,360,923,2382,6246,16486,43917,117692,317447,
%T A253013 860574,2344396,6413119,17611086,48527597,134141819,371862485,
%U A253013 1033588413,2879818379,8041870070,22503533295,63093284667,177213424466
%N A253013 a(n) = number of unlabeled rooted trees on n nodes with an even number of endpoints.
%H A253013 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 A253013 Marko Riedel, <a href="http://math.stackexchange.com/questions/1080099/">Unlabled rooted trees with even and odd numbers of endpoints</a>
%p A253013 T :=
%p A253013 proc(n)
%p A253013     option remember;
%p A253013     local k, s, A;
%p A253013     if n=0 then return 0 fi;
%p A253013     if n=1 then return u fi;
%p A253013     A := n -> add(subs(u=u^l, T(n/l))/l,
%p A253013                   l in divisors(n));
%p A253013     s := (1-u)*A(n-1);
%p A253013     s := s + 1/(n-1)*
%p A253013     add((k+1)*A(k+1)*T(n-1-k), k=0..n-2);
%p A253013     expand(s);
%p A253013 end;
%Y A253013 Cf. A000081, A253014.
%K A253013 nonn
%O A253013 1,4
%A A253013 _Marko Riedel_, Dec 25 2014