Generating function
$$U_{805}(x, y) = \frac{\left(1 - y\right)^{4} \left(- \frac{2 x}{\left(1 - y\right)^{2}} - \sqrt{- \frac{4 x}{\left(1 - y\right)^{2}} + 1} + 1\right)}{2 x^{2}}$$
Explicit formula
$$T_{805}(n, m, k) = \frac{k {\binom{2 k + 2 n}{n}} {\binom{m + 2 n - 1}{m}}}{k + n}$$
1 | 0 | 0 | 0 | 0 | 0 | 0 |
2 | 4 | 6 | 8 | 1 | 12 | 14 |
5 | 2 | 5 | 1 | 175 | 28 | 42 |
14 | 84 | 294 | 784 | 1764 | 3528 | 6468 |
42 | 336 | 1512 | 504 | 1386 | 33264 | 72072 |
132 | 132 | 726 | 2904 | 9438 | 264264 | 66066 |
429 | 5148 | 33462 | 156156 | 585585 | 1873872 | 5309304 |
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