$$U_{454}(x, y) = \frac{\left(y + 1\right)^{2} + \sqrt{4 x \left(y + 1\right) + \left(y + 1\right)^{4}}}{2 y + 2}$$

$$T_{454}(n, m, k) = \begin{cases}{\binom{k}{m}}&\text{if n=0} ,\ \\\frac{k {\binom{k - 3 n}{m}} {\binom{k - n - 1}{n - 1}}}{n} \end{cases} $$