Generating function
$$U_{666}(x, y) = \frac{\sqrt{4 x \left(y + 1\right)^{2} + 1} - 1}{2 x}$$
Explicit formula
$$T_{666}(n, m, k) = \frac{\left(-1\right)^{n} k {\binom{2 k + 2 n}{m}} {\binom{k + 2 n - 1}{n}}}{k + n}$$
| 1 | 2 | 1 | 0 | 0 | 0 | 0 |
| -1 | -4 | -6 | -4 | -1 | 0 | 0 |
| 2 | 12 | 3 | 4 | 3 | 12 | 2 |
| -5 | -4 | -14 | -28 | -35 | -28 | -14 |
| 14 | 14 | 63 | 168 | 294 | 3528 | 294 |
| -42 | -504 | -2772 | -924 | -2079 | -33264 | -38808 |
| 132 | 1848 | 12012 | 48048 | 132132 | 264264 | 396396 |
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