  Let $e_{n}^k$ be the entries in the classical Euler's difference table. We
consider the array $d_{n}^{k}=e_n^k/k!$ for $0\leq k \leq n$, where $d_n^k$ can
be interpreted as the number of k-fixed-points-permutations of [n]. We show
that the sequence $\{d_n^k\}_{0\leq k\leq n}$ is 2-log-concave and reverse
ultra log-concave for any given n.
