  We propose a conjecture on the generating series of Chern numbers of
tautological bundles on Hilbert schemes of points on curves and establish the
rank 1 and rank -1 case of this conjecture. Thus we compute explicitly the
generating series of integrals of the Segre classes of tautological bundles of
line bundles on curves, which has a similar structure as Lehn's conjecture for
surfaces.
