Generating function
$$U_{197}(x, y) = \frac{1 - \sqrt{y \left(4 x - 4\right) + 1}}{y \left(2 x^{2} - 4 x + 2\right)}$$
Explicit formula
$$T_{197}(n, m, k) = \frac{k {\binom{k + 2 m - 1}{m}} {\binom{k - m + n - 1}{n}}}{k + m}$$
| 1 | 1 | 2 | 5 | 14 | 42 | 132 |
| 1 | 0 | -2 | -1 | -42 | -168 | -66 |
| 1 | 0 | 0 | 5 | 42 | 252 | 132 |
| 1 | 0 | 0 | 0 | -14 | -168 | -132 |
| 1 | 0 | 0 | 0 | 0 | 42 | 66 |
| 1 | 0 | 0 | 0 | 0 | 0 | -132 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 |
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