$$U_{353}(x, y) = \left(1 - y\right)^{3} \left(x + \frac{1}{\left(1 - y\right)^{3}}\right)^{2}$$

$$T_{353}(n, m, k) = {\binom{2 k}{n}} {\binom{3 k + m - 3 n - 1}{m}}$$