Derangements and Euler’s difference table for C_S_n - Faliharimalala, Hilarion L. M.; Zeng, Jiang (The Electronic Journal of Combinatorics, 2008)
Euler’s difference table associated to the sequence {n!} leads naturally to the counting formula for the derangements. In this paper we study Euler’s difference table associated to the sequence {^n n!} and the generalized derangement problem. For the coefficients appearing in the later table we will give the combinatorial interpretations in terms of two kinds of k-successions of the group C_S_n. In particular for =1 we recover the known results for the symmetric groups while for =2 we obtain the corresponding results for the hyperoctahedral groups.