$$U_{521}(x, y) = \frac{- \sqrt{4 x + \left(y + 1\right)^{8}} + \left(y + 1\right)^{4}}{2 \left(y + 1\right)^{2}}$$

$$T_{521}(n, m, k) = \begin{cases}0&\text{if n<k} ,\ \\- \frac{k {\binom{2 k - 8 n}{m}} {\binom{k - n - 1}{n - 1}}}{n} \end{cases} $$