$$U_{529}(x, y) = \frac{- \sqrt{- \frac{4 x}{\left(1 - y\right)^{6}} + \frac{1}{\left(1 - y\right)^{8}}} + \frac{1}{\left(1 - y\right)^{4}}}{2 x}$$

$$T_{529}(n, m, k) = \frac{k {\binom{k + 2 n - 1}{n}} {\binom{2 k + m - 2 n - 1}{m}}}{k + n}$$