$$U_{341}(x, y) = \frac{\left(1 - \sqrt{1 - 4 y}\right) \left(- 2 x - \sqrt{1 - 4 x} + 1\right)}{4 x^{2} y}$$

$$T_{341}(n, m, k) = \frac{k^{2} {\binom{2 k + 2 n}{n}} {\binom{k + 2 m - 1}{m}}}{\left(k + m\right) \left(k + n\right)}$$