Generating function
$$U_{417}(x, y) = \frac{1}{\left(1 - x\right) \left(1 - y\right)^{2}}$$
Explicit formula
$$T_{417}(n, m, k) = \begin{cases}{\binom{k + n - 1}{n}} {\binom{2 k + m - 1}{m}},\ \\1&\text{if n<k } \end{cases} $$
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