Generating function
$$U_{857}(x, y) = \frac{\left(y + 1\right)^{5}}{- x + \left(y + 1\right)^{3}}$$
Explicit formula
$$T_{857}(n, m, k) = {\binom{2 k - 3 n}{m}} {\binom{k + n - 1}{n}}$$
| 1 | 2 | 1 | 0 | 0 | 0 | 0 |
| 1 | -1 | 1 | -1 | 1 | -1 | 1 |
| 1 | -4 | 1 | -2 | 35 | -56 | 84 |
| 1 | -7 | 28 | -84 | 21 | -462 | 924 |
| 1 | -1 | 55 | -22 | 715 | -2002 | 5005 |
| 1 | -13 | 91 | -455 | 182 | -6188 | 18564 |
| 1 | -16 | 136 | -816 | 3876 | -15504 | 54264 |
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