On the dynamics of the recursive sequence xn+1=αxn−1β+γ∑k=1txn−2k∏k=1txn−2k

In this paper, we investigate the global behavior of the difference equation xn+1=αxn−1β+γ∑k=1txn−2k∏k=1txn−2k,n=0,1,… where ββ is a positive parameter and αα, γγ are non-negative parameters, with non-negative initial conditions.