  We construct a series of conformally invariant differential operators acting
on weighted trace-free symmetric 2-tensors by a method similar to
Graham-Jenne-Mason-Sparling's. For compact conformal manifolds of dimension
even and greater than or equal to four with vanishing ambient obstruction
tensor, one of these operators is used to describe the second variation of the
total Q-curvature. An explicit formula for conformally Einstein manifolds is
given in terms of the Lichnerowicz Laplacian of an Einstein representative
metric.
