Generating function
$$U_{105}(x, y) = \frac{x^{2} - 2 x + y^{2} - 2 y + \left(x + y - 1\right) \sqrt{x^{2} - 2 x + y^{2} + y \left(- 2 x - 2\right) + 1} + 1}{2 x^{2} y^{2}}$$
Explicit formula
$$T_{105}(n, m, k) = \frac{2 k {\binom{2 k + m + n}{m}} {\binom{2 k + m + n}{2 k + m}}}{2 k + m + n}$$
1 | 2 | 3 | 4 | 5 | 6 | 7 |
2 | 8 | 2 | 4 | 7 | 112 | 168 |
3 | 2 | 75 | 21 | 49 | 1008 | 189 |
4 | 4 | 21 | 784 | 2352 | 6048 | 1386 |
5 | 7 | 49 | 2352 | 882 | 2772 | 7623 |
6 | 112 | 1008 | 6048 | 2772 | 104544 | 339768 |
7 | 168 | 189 | 1386 | 7623 | 339768 | 1288287 |
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