$$U_{832}(x, y) = \frac{- y^{2} + 2 y + \sqrt{- 4 x + y^{4} - 4 y^{3} + 6 y^{2} - 4 y + 1} - 1}{2 x y - 2 x}$$

$$T_{832}(n, m, k) = \frac{k {\binom{k + 2 n - 1}{n}} {\binom{3 k + m + 4 n - 1}{m}}}{k + n}$$