Log-Convexity and Fixed Points of Permutations

We provide a combinatorial proof for the fact that the numbers of derangements of length n form a log-convex sequence for n≥3. A minor modification of our proof yields the same result for permutations of length n≥4 that have exactly one fixed point. We explain why these statements do not generalize for permutations with exactly k fixed points where k≥3.