Generating function
$$U_{847}(x, y) = \frac{1}{x y^{5} - 5 x y^{4} - x + y^{3} \left(10 x - 1\right) + y^{2} \left(3 - 10 x\right) + y \left(5 x - 3\right) + 1}$$
Explicit formula
$$T_{847}(n, m, k) = {\binom{k + n - 1}{n}} {\binom{3 k + m - 2 n - 1}{m}}$$
| 1 | 3 | 6 | 1 | 15 | 21 | 28 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 1 | -1 | 0 | 0 | 0 | 0 | 0 |
| 1 | -3 | 3 | -1 | 0 | 0 | 0 |
| 1 | -5 | 1 | -1 | 5 | -1 | 0 |
| 1 | -7 | 21 | -35 | 35 | -21 | 7 |
| 1 | -9 | 36 | -84 | 126 | -126 | 84 |
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