Generating function
$$U_{396}(x, y) = \frac{\sqrt{\frac{4 x}{\sqrt{1 - 4 y}} + \frac{1}{1 - 4 y}}}{2} + \frac{1}{2 \sqrt{1 - 4 y}}$$
Explicit formula
$$T_{396}(n, m, k) = \begin{cases}4^{m} {\binom{\frac{k}{2} + m - 1}{m}}&\text{if n=0} ,\ \\\frac{4^{m} k {\binom{k - n - 1}{n - 1}} {\binom{\frac{k}{2} + m - \frac{n}{2} - 1}{m}}}{n} \end{cases} $$
1 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 0 | 0 | 0 | 0 | 0 | 0 |
-1 | 0 | 0 | 0 | 0 | 0 | 0 |
2 | -8 | 0 | 0 | 0 | 0 | 0 |
-5 | 2 | 0 | 0 | 0 | 0 | 0 |
14 | -112 | 224 | 0 | 0 | 0 | 0 |
-42 | 336 | -672 | 0 | 0 | 0 | 0 |
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