On recent Partition function of Kaur and Rana

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