$$U_{532}(x, y) = \frac{\left(1 - y\right)^{2} \left(\sqrt{4 x + \frac{1}{\left(1 - y\right)^{8}}} + \frac{1}{\left(1 - y\right)^{4}}\right)}{2}$$

$$T_{532}(n, m, k) = \begin{cases}{\binom{2 k + m - 1}{m}}&\text{if n==0 } ,\ \\\frac{k {\binom{k - n - 1}{n - 1}} {\binom{2 k + m - 8 n - 1}{m}}}{n}&\text{if n>0} \end{cases} $$