The main purpose of this paper is to derive the closed form solution the sequence (g n) n∈N of integro-difference equations that is defined recursively as follows: g 1 (x) = χ (−1/2,1/2) (x), g n+1 (x) = g n (x + 1/2) − g n (x − 1/2) + x+ 1 g n (s)ds, n ∈ N, where g 1 (x) = χ (−1/2,1/2) (x) is the characteristic function of the unit interval (−1/2, 1/2) has value equal to 1 on (−1/2, 1/2) and 0 elsewhere in R.