$$U_{1463}(x, y) = \frac{- 2 x \left(y + 1\right)^{3} - \sqrt{- 4 x \left(y + 1\right)^{3} + 1} + 1}{2 x^{2} \left(y + 1\right)^{4}}$$

$$T_{1463}(n, m, k) = \frac{k {\binom{2 k + 2 n}{n}} {\binom{2 k + 3 n}{m}}}{k + n}$$