Generating function
$$U_{140}(x, y) = \frac{- y + \sqrt{4 x + y^{2} + y \left(4 x + 2\right) + 1} - 1}{2 x y + 2 x}$$
Explicit formula
$$T_{140}(n, m, k) = \frac{\left(-1\right)^{m + n} k {\binom{k + 2 n - 1}{n}} {\binom{k + m + n - 1}{m}}}{k + n}$$
1 | -1 | 1 | -1 | 1 | -1 | 1 |
-1 | 2 | -3 | 4 | -5 | 6 | -7 |
2 | -6 | 12 | -2 | 3 | -42 | 56 |
-5 | 2 | -5 | 1 | -175 | 28 | -42 |
14 | -7 | 21 | -49 | 98 | -1764 | 294 |
-42 | 252 | -882 | 2352 | -5292 | 10584 | -19404 |
132 | -924 | 3696 | -11088 | 2772 | -60984 | 121968 |
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