Generating function
$$U_{332}(x, y) = \frac{\left(1 - \sqrt{1 - 4 x}\right) \left(\sqrt{4 y + 1} + 1\right)}{4 x}$$
Explicit formula
$$T_{332}(n, m, k) = \begin{cases}\frac{k {\binom{k + 2 n - 1}{n}}}{k + n}&\text{if m=0} ,\ \\\frac{\left(-1\right)^{m - 1} k^{2} {\binom{- k + 2 m - 1}{m - 1}} {\binom{k + 2 n - 1}{n}}}{m \left(k + n\right)} \end{cases} $$
| 1 | 1 | -1 | 2 | -5 | 14 | -42 |
| 1 | 1 | -1 | 2 | -5 | 14 | -42 |
| 2 | 2 | -2 | 4 | -1 | 28 | -84 |
| 5 | 5 | -5 | 1 | -25 | 7 | -21 |
| 14 | 14 | -14 | 28 | -7 | 196 | -588 |
| 42 | 42 | -42 | 84 | -21 | 588 | -1764 |
| 132 | 132 | -132 | 264 | -66 | 1848 | -5544 |
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