Let K be a field, n ≥ 2 an integer, and Rn= K[Xn, Xn+1,…,X2n−1]. In this paper, we study lengths of factorizations in Rn. For any atomic domain D, define ρ(D) = sup{ r/s ∣ X1…xr= y1…ys, xi, yj∈ D irreducible } and φ(r) = ∣{ m ∣ X1…xr= y1…ym, xi, yj∈ D irreducible }∣. We show that ρ(Rn)| =(nD(Gn(K)) + 3n − 2)/(2n), where D(Gn(K)) is the Davenport constant of an abelian group Gn(K) associated with K. Hence ρ(Rn) is finite if and only if K is finite. If K is finite, we also show that for Rn,.