$$U_{515}(x, y) = \frac{- \sqrt{4 x + \left(y + 1\right)^{4}} + \left(y + 1\right)^{2}}{2 y + 2}$$

$$T_{515}(n, m, k) = \begin{cases}0&\text{if n<k } ,\ \\- \frac{k {\binom{k - 4 n}{m}} {\binom{k - n - 1}{n - 1}}}{n} \end{cases} $$