  The problem of counting derangements was initiated by Pierre Remonde de
Motmort in 1708. A derangement is a permutation that has no fixed points and
the derangement number Dn is the number of fixed point free permutations on an
n element set. Furthermore, the derangement polynomials are natural extensions
of the derangement numbers. In this paper, we study the derangement polynomials
and numbers, their connections with cosine-derangement polynomials and
sine-derangement polynomials and their applications to moments of some variants
of gamma random variables.
