In this paper, we consider the doubly indexed sequence a (r) λ (n, m), (n, m ≥ 0), defined by a recurrence relation and an initial sequence a (r) λ (0, m), (m ≥ 0). We derive with the help of some differential operator an explicit expression for a (r) λ (n, 0), in term of the degenerate r-Stirling numbers of the second kind and the initial sequence. We observe that a (r) λ (n, 0) = β n,λ (r), for a (r) λ (0, m) = 1 m+1 , and a (r) λ (n, 0) = E n,λ (r), for a (r) λ (0, m) = 1 2 m. Here β n,λ (x) and E n,λ (x) are the fully degenerate Bernoulli polynomials and the degenerate Euler polynomials, respectively.