Generating function
$$U_{1060}(x, y) = \frac{\left(1 - \sqrt{1 - 4 x}\right)^{2} \left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{2}}{16 x^{2} y^{4}}$$
Explicit formula
$$T_{1060}(n, m, k) = \frac{4 k^{2} {\binom{4 k + 2 m}{m}} {\binom{2 k + 2 n - 1}{n}}}{\left(2 k + m\right) \left(2 k + n\right)}$$
1 | 4 | 14 | 48 | 165 | 572 | 2002 |
2 | 8 | 28 | 96 | 33 | 1144 | 4004 |
5 | 2 | 7 | 24 | 825 | 286 | 1001 |
14 | 56 | 196 | 672 | 231 | 8008 | 28028 |
42 | 168 | 588 | 2016 | 693 | 24024 | 84084 |
132 | 528 | 1848 | 6336 | 2178 | 75504 | 264264 |
429 | 1716 | 6006 | 20592 | 70785 | 245388 | 858858 |
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