Compositions inside a rectangle and unimodality

Let c ^k,l (n) be the number of compositions (ordered partitions) of the integer n whose Ferrers diagram fits inside a k×l rectangle. The purpose of this note is to give a simple, algebraic proof of a conjecture of Vatter that the sequence c ^k,l (0),c ^k,l (1),…,c ^k,l (kl) is unimodal. The problem of giving a combinatorial proof of this fact is discussed, but is still open.