$$U_{565}(x, y) = \frac{1 - \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{- x}}{2} \right)}}{3} \right)}}{3}}{\left(1 - y\right)^{2}}$$

$$T_{565}(n, m, k) = \begin{cases}{\binom{2 k + m - 1}{m}}&\text{if n==0} ,\ \\\frac{\left(-1\right)^{n - 1} k {\binom{- k + 3 n - 1}{n - 1}} {\binom{2 k + m - 1}{m}}}{n}&\text{if n>0} \end{cases} $$