Generating function
$$U_{16}(x, y) = \frac{1 - \sqrt{- 4 x y^{2} - 8 x y - 4 x + 1}}{2 x \left(y + 1\right)}$$
Explicit formula
$$T_{16}(n, m, k) = \frac{k {\binom{k + 2 n}{m}} {\binom{k + 2 n}{n}}}{k + 2 n}$$
| 1 | 1 | 0 | 0 | 0 | 0 | 0 |
| 1 | 3 | 3 | 1 | 0 | 0 | 0 |
| 2 | 1 | 2 | 2 | 1 | 2 | 0 |
| 5 | 35 | 105 | 175 | 175 | 105 | 35 |
| 14 | 126 | 504 | 1176 | 1764 | 1764 | 1176 |
| 42 | 462 | 231 | 693 | 1386 | 19404 | 19404 |
| 132 | 1716 | 10296 | 37752 | 9438 | 169884 | 226512 |
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