Generating function
$$U_{1086}(x, y) = \frac{\left(1 - \sqrt{1 - 4 y}\right)^{3} \left(- 2 x - \sqrt{1 - 4 x} + 1\right)^{2}}{32 x^{4} y^{3}}$$
Explicit formula
$$T_{1086}(n, m, k) = \frac{6 k^{2} {\binom{4 k + 2 n}{n}} {\binom{3 k + 2 m - 1}{m}}}{\left(2 k + n\right) \left(3 k + m\right)}$$
Data table
1 3 9 28 9 297 1001
4 12 36 112 36 1188 4004
14 42 126 392 126 4158 14014
48 144 432 1344 432 14256 48048
165 495 1485 462 1485 49005 165165
572 1716 5148 16016 5148 169884 572572
2002 6006 18018 56056 18018 594594 2004002
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