Generating function
$$U_{53}(x, y) = \frac{- \sqrt{4 y + 1} - 1}{2 x - 2}$$
Explicit formula
$$T_{53}(n, m, k) = \begin{cases}1&\text{if m=0} ,\ \\\frac{k {\binom{k - m - 1}{m - 1}} {\binom{k + n - 1}{n}}}{m} \end{cases} $$
| 1 | 1 | -1 | 2 | -5 | 14 | -42 |
| 1 | 1 | -1 | 2 | -5 | 14 | -42 |
| 1 | 1 | -1 | 2 | -5 | 14 | -42 |
| 1 | 1 | -1 | 2 | -5 | 14 | -42 |
| 1 | 1 | -1 | 2 | -5 | 14 | -42 |
| 1 | 1 | -1 | 2 | -5 | 14 | -42 |
| 1 | 1 | -1 | 2 | -5 | 14 | -42 |
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