In his recent paper on partitions (1), Jakub Intrator proved that the number p(n, k) of partitions of n into exactly k summands, 1 < k ≦ n, is given by a polynomial of degree exactly k − 1 in n, the first [(k+1)/2] coefficients of which (starting with the coefficient of the highest degree term), are independent of n and the rest depend on the residue of n modulo the least common multiple of the integers 1, 2, 3, …, k. He even showed (ignoring the case k = 3) that the [(k+3)/2]-th coefficient in the polynomial depends only on the parity of n and is not the same for n even and n odd.