$$U_{455}(x, y) = \frac{\left(y + 1\right)^{2} - \sqrt{4 x \left(y + 1\right) + \left(y + 1\right)^{4}}}{2 y + 2}$$

$$T_{455}(n, m, k) = \begin{cases}0&\text{if n<k} ,\ \\- \frac{k {\binom{k - 3 n}{m}} {\binom{k - n - 1}{n - 1}}}{n} \end{cases} $$