$$U_{39}(x, y) = \frac{1 - \sqrt{- 4 x y - 4 x + 1}}{x \left(2 y + 2\right)}$$

$$T_{39}(n, m, k) = \frac{k {\binom{k + 2 n - 1}{m}} {\binom{k - m + 2 n - 1}{k + n - 1}}}{k + n}$$