$$U_{291}(x, y) = \frac{\sqrt{3} \left(\sqrt{2 \sqrt{3} x \sqrt{y} \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)} + \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}} + \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}\right)}{3 \sqrt{y}}$$

$$T_{291}(n, m, k) = \begin{cases}1&\text{if n=0 and m=0} ,\ \\\frac{\left(-1\right)^{n - 1} k {\binom{- k + 2 n - 1}{n - 1}}}{n}&\text{if n>0 and m=0} ,\ \\\frac{\left(-1\right)^{m + 1} k {\binom{k - n}{n}} {\binom{- k - 2 m + n - 1}{m - 1}}}{m} \end{cases} $$