$$U_{340}(x, y) = \frac{- y \left(2 x + 2\right) - \sqrt{y \left(4 x^{2} + 4 x\right) + 1} + 1}{2 y^{2} - 2 y}$$

$$T_{340}(n, m, k) = \frac{k {\binom{2 k + 2 m}{n}} {\binom{k + m - n}{m}}}{k + m}$$