Sequences And Series

Let \(S_{K}=\frac{1+2+\ldots+K}{K}\) and \(\sum_\limits{j=1}^{n} S_{j}^{2}=\frac{n}{A}\left(B n^{2}+C n+D\right)\), where \(A, B, C, D \in \mathbb{N}\) and \(A\) has least value. Then