Consider a sequence $\{a_n\}$ $(n = 1, 2, 3, \cdots)$ where the sum of the first $n$ terms is
$$\sum_{k=1}^{n} a_k = n^2 + 3n$$
(1) Then $a_n = \mathbf{A}\, n + \mathbf{B}$.
(2) For the sequence $\{b_n\}$ $(n = 1, 2, 3, \cdots)$, where $b_n = n^2 - 5n - 6$, the number of terms satisfying $b_n < 0$ is $\mathbf{C}$, and the sum of such terms is $-\mathbf{DE}$.
(3) It follows that for the sequences $\{a_n\}$ and $\{b_n\}$ in (1) and (2),
$$\sum_{k=1}^{n} \frac{k^2 b_k}{a_k} = \frac{1}{\mathbf{F}}\, n(n + \mathbf{G})\left(n^2 - \mathbf{H}\, n - \mathbf{I}\right).$$