Generating function
$$U_{70}(x, y) = \frac{1}{- x + \left(1 - y\right)^{2}}$$
Explicit formula
$$T_{70}(n, m, k) = {\binom{k + n - 1}{n}} {\binom{2 k + m + 2 n - 1}{m}}$$
| 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| 1 | 4 | 1 | 2 | 35 | 56 | 84 |
| 1 | 6 | 21 | 56 | 126 | 252 | 462 |
| 1 | 8 | 36 | 12 | 33 | 792 | 1716 |
| 1 | 1 | 55 | 22 | 715 | 2002 | 5005 |
| 1 | 12 | 78 | 364 | 1365 | 4368 | 12376 |
| 1 | 14 | 105 | 56 | 238 | 8568 | 27132 |
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