$$U_{803}(x, y) = \frac{- 2 x \left(y + 1\right)^{2} - \sqrt{- 4 x \left(y + 1\right)^{2} + 1} + 1}{2 x^{2} \left(y + 1\right)^{2}}$$

$$T_{803}(n, m, k) = \frac{k {\binom{2 k + 2 n}{m}} {\binom{2 k + 2 n}{n}}}{k + n}$$