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
$$T_{1085}(n, m, k) = \frac{4 k^{2} {\binom{4 k + 2 n}{n}} {\binom{2 k + 2 m - 1}{m}}}{\left(2 k + m\right) \left(2 k + n\right)}$$
Data table
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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