Generating function
$$U_{141}(x, y) = \frac{- x + \sqrt{x^{2} + 2 x + y \left(4 x + 4\right) + 1} - 1}{y \left(2 x + 2\right)}$$
Explicit formula
$$T_{141}(n, m, k) = \frac{\left(-1\right)^{m + n} k {\binom{k + 2 m - 1}{m}} {\binom{k + m + n - 1}{n}}}{k + m}$$
| 1 | -1 | 2 | -5 | 14 | -42 | 132 |
| -1 | 2 | -6 | 2 | -7 | 252 | -924 |
| 1 | -3 | 12 | -5 | 21 | -882 | 3696 |
| -1 | 4 | -2 | 1 | -49 | 2352 | -11088 |
| 1 | -5 | 3 | -175 | 98 | -5292 | 2772 |
| -1 | 6 | -42 | 28 | -1764 | 10584 | -60984 |
| 1 | -7 | 56 | -42 | 294 | -19404 | 121968 |
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