Generating function
$$U_{66}(x, y) = \frac{1 - \sqrt{1 - 4 y}}{x \sqrt{1 - 4 y} - x + 2 y}$$
Explicit formula
$$T_{66}(n, m, k) = \frac{k {\binom{k + n}{n}} {\binom{k + 2 m + n - 1}{m}}}{k + m + n}$$
| 1 | 1 | 2 | 5 | 14 | 42 | 132 |
| 1 | 2 | 5 | 14 | 42 | 132 | 429 |
| 1 | 3 | 9 | 28 | 9 | 297 | 1001 |
| 1 | 4 | 14 | 48 | 165 | 572 | 2002 |
| 1 | 5 | 2 | 75 | 275 | 1001 | 364 |
| 1 | 6 | 27 | 11 | 429 | 1638 | 6188 |
| 1 | 7 | 35 | 154 | 637 | 2548 | 9996 |
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