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