Abstract:  For 0 ≤ k ≤ n, let e^k_n be the entries in Euler's difference table and let d^k_n = e^k_n/k!. Dumont and Randrianarivony showed e^k_n equals the number of permutations on [n] whose fixed points are contained in {1, 2,..., k}. Rakotondrajao found a combinatorial interpretation of the number d^k_n in terms of k-fixed-points-permutations of [n]. We show that for any n ≥ 1, the sequence {d^k_n}_{0 ≤k≤n} is both 2-log-concave and reverse ultra logconcave.

  AMS Classification:  05A20, 05A10

  Keywords:  log-concavity, 2-log-concavity, reverse ultra log-concavity, Euler's difference table

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