$$U_{865}(x, y) = \frac{1 - \sqrt{- 4 x \left(1 - y\right) + 1}}{2 x \left(1 - y\right)^{3}}$$

$$T_{865}(n, m, k) = \frac{k {\binom{k + 2 n - 1}{n}} {\binom{2 k + m - n - 1}{m}}}{k + n}$$