$$U_{511}(x, y) = \frac{\left(y + 1\right)^{2} - \sqrt{- 4 x \left(y + 1\right)^{3} + \left(y + 1\right)^{4}}}{2 x}$$

$$T_{511}(n, m, k) = \frac{k {\binom{k - n}{m}} {\binom{k + 2 n - 1}{n}}}{k + n}$$