Sloane's box stacking problem

Recently, Sloane suggested the following problem: We are given n boxes, labeled 1, 2, . . . , n. For i = 1, . . . , n, box i weighs (m − 1)i grams (where m ≥ 2 is a fixed integer) and box i can support a total weight of i grams. What is the number of different ways to build a single stack of boxes in which no box will be squashed by the weight of the boxes above it? Prior to this generalized problem, Sloane & Sellers solved the case m = 2. More recently, Andrews & Sellers solved the case m ≥ 3. In this note we give new and simple proofs of the results of Sloane & Sellers and of Andrews & Sellers, using a known connection with m-ary partitions.