  G. Andrews proved that if $n$ is a prime number then the coefficients $a_k$
and $a_{k+n}$ of the product $(q,q)_\infty/(q^n,q^n)_\infty=\sum_k a_kq^k$ have
the same sign, see [A1]. We generalize this result in several directions. Our
results are based on the observation that many products can be written as
alternating sums of characters of Virasoro modules.
