Generating function
$$U_{700}(x, y) = \frac{1}{- \frac{x \left(- 2 y - \sqrt{1 - 4 y} + 1\right)}{2 y^{2}} + 1}$$
Explicit formula
$$T_{700}(n, m, k) = \frac{n {\binom{2 m + 2 n}{m}} {\binom{k + n - 1}{n}}}{m + n}$$
| nan | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 2 | 5 | 14 | 42 | 132 | 429 |
| 1 | 4 | 14 | 48 | 165 | 572 | 2002 |
| 1 | 6 | 27 | 11 | 429 | 1638 | 6188 |
| 1 | 8 | 44 | 208 | 91 | 3808 | 15504 |
| 1 | 1 | 65 | 35 | 17 | 7752 | 33915 |
| 1 | 12 | 9 | 544 | 2907 | 14364 | 67298 |
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