  We develop a method for counting words subject to various restrictions by
finding a combinatorial interpretation for a product of weighted sums of
Laguerre polynomials with parameter \alpha = -1. We describe how such a series
can be computed by finding an appropriate ordinary generating function and
applying a certain transformation. We use this technique to find the generating
function for the number of k-ary words avoiding any vincular pattern that has
only ones, as well as words cyclically avoiding vincular patterns with only
ones whose runs of ones between dashes are all of equal length.
