On recent Partition function of Kaur and Rana

Abstract

Recently, Kaur and Rana introduced the partition function denoted by $\ddot{I}(n)$, where the largest part $\hat{I}»$ appears exactly once, and the remaining parts constitute a partition of $\hat{I}»$. In this paper, we establish new generating functions for certain variants of $\ddot{I}(n)$. Further, we obtain a linear recurrence relation for our new generating function.

9 pages