$$U_{135}(x, y) = \left(x + y\right)^{4}$$

$$\delta{(a, b)} = \begin{cases}1&\text{if a = b},\\ 0 \end{cases} $$$$T_{135}(n, m, k) = \delta{\left(4 k,m + n \right)} {\binom{m + n}{m}}$$