Generating function
$$U_{161}(x, y) = \frac{x - \sqrt{x^{2} - 2 x + 4 y + 1} - 1}{2 x - 2}$$
Explicit formula
$$T_{161}(n, m, k) = \begin{cases}1&\text{if n=0,m=0} ,\ \\0&\text{if m=0} ,\ \\\frac{\left(-1\right)^{m - 1} k {\binom{- k + 2 m - 1}{m - 1}} {\binom{2 m + n - 1}{n}}}{m} \end{cases} $$
| 1 | 1 | -1 | 2 | -5 | 14 | -42 |
| 0 | 2 | -4 | 12 | -4 | 14 | -504 |
| 0 | 3 | -1 | 42 | -18 | 77 | -3276 |
| 0 | 4 | -2 | 112 | -6 | 308 | -15288 |
| 0 | 5 | -35 | 252 | -165 | 1001 | -5733 |
| 0 | 6 | -56 | 504 | -396 | 28028 | -183456 |
| 0 | 7 | -84 | 924 | -858 | 7007 | -519792 |
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