$$U_{1457}(x, y) = \frac{\left(1 - y\right) \left(- \frac{2 x}{\left(1 - y\right)^{2}} - \sqrt{- \frac{4 x}{\left(1 - y\right)^{2}} + 1} + 1\right)}{2 x^{2}}$$

$$T_{1457}(n, m, k) = \frac{k {\binom{2 k + 2 n}{n}} {\binom{3 k + m + 2 n - 1}{m}}}{k + n}$$