$$U_{1233}(x, y) = \frac{\left(\frac{x}{\left(1 - y\right)^{2}} + 1\right)^{3}}{\left(1 - y\right)^{2}}$$

$$T_{1233}(n, m, k) = {\binom{3 k}{n}} {\binom{2 k + m + 2 n - 1}{m}}$$