Generating function
$$U_{434}(x, y) = \frac{x^{2} - 2 x + y + 1}{x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 1}$$
Explicit formula
$$T_{434}(n, m, k) = {\binom{k}{m}} {\binom{2 k + 2 m + n - 1}{n}}$$
| 1 | 1 | 0 | 0 | 0 | 0 | 0 |
| 2 | 4 | 0 | 0 | 0 | 0 | 0 |
| 3 | 1 | 0 | 0 | 0 | 0 | 0 |
| 4 | 2 | 0 | 0 | 0 | 0 | 0 |
| 5 | 35 | 0 | 0 | 0 | 0 | 0 |
| 6 | 56 | 0 | 0 | 0 | 0 | 0 |
| 7 | 84 | 0 | 0 | 0 | 0 | 0 |
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