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%I #13 Sep 22 2015 12:09:45
%S 1,1,0,1,0,1,1,3,2,5,5,13,13,29,32,71,81,177,209,449,538,1148,1415,
%T 3002,3736,7862,9930,20877,26648,55756,71767,149860,194507,405332,
%U 529708,1101502,1447956,3006750,3974959,8242691,10948355,22673357,30249668,62583402,83831176,173259448,232917913,480970826,648753720
%N Difference between the numbers of trees on n vertices with an even number and an odd number of leaves.
%C The sequence could be prepended with a(0)=1 and a(1)=-1. However, it is conjectured that for all n>=2, we have a(n)>=0 (cf. MathOverflow link).
%H MathOverflow, <a href="http://mathoverflow.net/questions/218394/counting-trees-according-to-endpoints">Counting trees according to endpoints</a>, 2015.
%F a(n) = A262430(n) - A262431(n).
%F G.f.: x + A(x,-1), where A(x,y) is g.f. for A055290.
%Y Cf. A055290, A055277.
%K nonn
%O 2,8
%A _Max Alekseyev_, Sep 21 2015