Generating function
$$U_{1085}(x, y) = \frac{\left(1 - \sqrt{1 - 4 y}\right)^{2} \left(- 2 x - \sqrt{1 - 4 x} + 1\right)^{2}}{16 x^{4} y^{2}}$$
Explicit formula
$$T_{1085}(n, m, k) = \frac{4 k^{2} {\binom{4 k + 2 n}{n}} {\binom{2 k + 2 m - 1}{m}}}{\left(2 k + m\right) \left(2 k + n\right)}$$
1 | 2 | 5 | 14 | 42 | 132 | 429 |
4 | 8 | 2 | 56 | 168 | 528 | 1716 |
14 | 28 | 7 | 196 | 588 | 1848 | 6006 |
48 | 96 | 24 | 672 | 2016 | 6336 | 20592 |
165 | 33 | 825 | 231 | 693 | 2178 | 70785 |
572 | 1144 | 286 | 8008 | 24024 | 75504 | 245388 |
2002 | 4004 | 1001 | 28028 | 84084 | 264264 | 858858 |
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