Let \(T(m,n)\) denote the number of \(m \times n\) rectangular standard Young tableaux with the property that the difference of any two rows has all entries equal. Let \(T(n) = \sum\limits_{d|n} T(d,n/d)\). We find recurrence relations satisfied by the numbers \(T(m,n)\) and \(\hat{T}(n)\), compute their generating functions, and express them explicitly in some special cases.