$$U_{977}(x, y) = 1 - \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{- x \left(y + 1\right)}}{2} \right)}}{3} \right)}}{3}$$

$$T_{977}(n, m, k) = \begin{cases}{\binom{n}{m}}&\text{if n = 0} ,\ \\\frac{\left(-1\right)^{n - 1} k {\binom{n}{m}} {\binom{- k + 3 n - 1}{n - 1}}}{n} \end{cases} $$