ON SUMS WITH THE r-DERANGEMENT NUMBERS

Abstract

In this paper, we derive some sums involving the r-derangement numbers, D_r (n) and the generalized hyperharmonic numbers of order r, H_n^r (α) by using the generating functions and Riordan arrays. For example, for n,r∈Z^+with n≥r, ∑_(i=0)^(n-r)〖(-1)^i ((r+1i)) (D_r (n-i))/(n-i)!〗=(-1)^(n-r)/(n-r)!.