Generating function
$$U_{106}(x, y) = \frac{x^{2} + y^{2} + y \left(- 2 x - 2\right) + \left(- x + y - 1\right) \sqrt{x^{2} - 2 x + y^{2} + y \left(- 2 x - 2\right) + 1} + 1}{2 x^{2}}$$
Explicit formula
$$T_{106}(n, m, k) = \frac{2 k {\binom{2 k + m + n}{m}} {\binom{m + n - 1}{n}}}{2 k + m + n}$$
1 | 2 | 3 | 4 | 5 | 6 | 7 |
0 | 2 | 8 | 2 | 4 | 7 | 112 |
0 | 2 | 15 | 6 | 175 | 42 | 882 |
0 | 2 | 24 | 14 | 56 | 1764 | 4704 |
0 | 2 | 35 | 28 | 147 | 588 | 19404 |
0 | 2 | 48 | 504 | 336 | 16632 | 66528 |
0 | 2 | 63 | 84 | 693 | 4158 | 198198 |
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