A262395 Difference between the numbers of trees on n vertices with an even number and an odd number of leaves.

1, 1, 0, 1, 0, 1, 1, 3, 2, 5, 5, 13, 13, 29, 32, 71, 81, 177, 209, 449, 538, 1148, 1415, 3002, 3736, 7862, 9930, 20877, 26648, 55756, 71767, 149860, 194507, 405332, 529708, 1101502, 1447956, 3006750, 3974959, 8242691, 10948355, 22673357, 30249668, 62583402, 83831176, 173259448, 232917913, 480970826, 648753720

Offset: 2

Author

Max Alekseyev, Sep 21 2015

Keywords

• nonn

Comments

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).

Links

• MathOverflow, Counting trees according to endpoints, 2015.

Crossrefs

Cf. A055290, A055277.

Formula

a(n) = A262430(n) - A262431(n).

G.f.: x + A(x,-1), where A(x,y) is g.f. for A055290.