Generating function
$$U_{124}(x, y) = \frac{x - \sqrt{x^{2} - 2 x + y \left(4 x - 4\right) + 1} - 1}{2 x - 2}$$
Explicit formula
$$T_{124}(n, m, k) = \begin{cases}1&\text{if n=0, m=0} ,\ \\0&\text{if m=0} ,\ \\- \frac{k {\binom{- k + 2 m - 1}{m - 1}} {\binom{m + n - 1}{n}}}{m}&\text{if m>0} \end{cases} $$
| 1 | -1 | -1 | -2 | -5 | -14 | -42 |
| 0 | -1 | -2 | -6 | -2 | -7 | -252 |
| 0 | -1 | -3 | -12 | -5 | -21 | -882 |
| 0 | -1 | -4 | -2 | -1 | -49 | -2352 |
| 0 | -1 | -5 | -3 | -175 | -98 | -5292 |
| 0 | -1 | -6 | -42 | -28 | -1764 | -10584 |
| 0 | -1 | -7 | -56 | -42 | -294 | -19404 |
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