Probability That All Faces Appear in Consecutive Rolls

You roll a fair 6-sided die $n$ times, producing a sequence of outcomes $X_1, X_2, \ldots, X_n$. A "window" is any block of 6 consecutive rolls $X_i, X_{i+1}, \ldots, X_{i+5}$. What is the probability that at least one window contains all six faces (i.e., is a permutation of $\{1, 2, 3, 4, 5, 6\}$)?