A refinement of a result of Andrews and Newman on the sum of minimal excludants

Abstract: We find an interesting refinement of a result due to Andrews and Newman, that is, the sum of minimal excludants over all the partitions of a number $n$ equals the number of distinct parts partitions of $n$ into two colors. In addition, we also study $k^{th}$ moments of minimal excludants by means of generalizing the aforementioned result. At the end, we also provide an alternate proof of a beautiful identity due to Hopkins, Sellers and Stanton.