Generating function
$$U_{126}(x, y) = \frac{2 x y + \sqrt{y^{2} \left(4 x^{2} + 1\right) - 2 y + 1}}{\left(1 - y\right)^{2}}$$
Explicit formula
$$T_{126}(n, m, k) = \frac{4^{n} k {\binom{\frac{k}{2} + \frac{n}{2}}{n}} {\binom{k + m}{k + n}}}{k + m}$$
1 | 1 | 1 | 1 | 1 | 1 | 1 |
0 | 2 | 4 | 6 | 8 | 1 | 12 |
0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 |
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