  We study the integer sequence v_n of numbers of lines in hypersurfaces of
degree 2n-3 of P^n, n>1. We prove a number of congruence properties of these
numbers of several different types. Furthermore, the asymptotics of the v_n are
described (in an appendix by Don Zagier). An attempt is made at a similar
analysis of two other enumerative sequences: the number of rational plane
curves and the number of instantons in the quintic threefold.
