$$U_{150}(x, y) = \frac{- 2 x - \sqrt{- 4 x y - 4 x + 1} + 1}{2 x}$$

$$T_{150}(n, m, k) = \begin{cases}0&\text{if m+n<k or m+n=0} ,\ \\\frac{k {\binom{2 n}{- k + m + n}} {\binom{m + n}{n}}}{m + n} \end{cases} $$