$$U_{840}(x, y) = \frac{\left(1 - \sqrt{- 4 x \left(y + 1\right) + 1}\right) \left(y + 1\right)}{2 x}$$

$$T_{840}(n, m, k) = \frac{k {\binom{2 k + n}{m}} {\binom{k + 2 n - 1}{n}}}{k + n}$$