$$U_{373}(x, y) = \frac{\left(1 - \sqrt{1 - 4 x}\right) \left(y + 1\right)^{2}}{2 x}$$

$$T_{373}(n, m, k) = \frac{k {\binom{2 k}{m}} {\binom{k + 2 n - 1}{n}}}{k + n}$$