Generating function
$$U_{167}(x, y) = \frac{- x - 1}{y \left(x^{2} + 2 x + 1\right) - 1}$$
Explicit formula
$$T_{167}(n, m, k) = {\binom{k + 2 m}{n}} {\binom{k + m - 1}{m}}$$
| 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 1 | 3 | 5 | 7 | 9 | 11 | 13 |
| 0 | 3 | 1 | 21 | 36 | 55 | 78 |
| 0 | 1 | 1 | 35 | 84 | 165 | 286 |
| 0 | 0 | 5 | 35 | 126 | 33 | 715 |
| 0 | 0 | 1 | 21 | 126 | 462 | 1287 |
| 0 | 0 | 0 | 7 | 84 | 462 | 1716 |
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