$$U_{609}(x, y) = \left(1 - 4 y\right) \left(x + \frac{1}{\left(1 - 4 y\right)^{\frac{3}{2}}}\right)$$

$$T_{609}(n, m, k) = 4^{m} {\binom{k}{n}} {\binom{\frac{k}{2} + m - \frac{3 n}{2} - 1}{m}}$$