Generating function
$$U_{869}(x, y) = \frac{1 - \sqrt{- 4 x \left(1 - y\right)^{2} + 1}}{2 x \left(1 - y\right)^{5}}$$
Explicit formula
$$T_{869}(n, m, k) = \frac{k {\binom{k + 2 n - 1}{n}} {\binom{3 k + m - 2 n - 1}{m}}}{k + n}$$
| 1 | 3 | 6 | 1 | 15 | 21 | 28 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 2 | -2 | 0 | 0 | 0 | 0 | 0 |
| 5 | -15 | 15 | -5 | 0 | 0 | 0 |
| 14 | -7 | 14 | -14 | 7 | -14 | 0 |
| 42 | -294 | 882 | -147 | 147 | -882 | 294 |
| 132 | -1188 | 4752 | -11088 | 16632 | -16632 | 11088 |
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