On the number of partitions into parts of k different magnitudes

Recently, the number of partitions of the positive integer n that have exactly k distinct values for the parts has been expressed in terms of the number of partitions of n into exactly k distinct parts, q(n,k). In this paper, the authors considered some tools from symmetric functions theory and derived a recurrence relation for the number of partitions of the positive integer n that have exactly k distinct values for the parts. This recurrence relation does not involve other partition functions.