Generating function
$$U_{1164}(x, y) = \frac{16 y^{6} \left(1 - \sqrt{- \frac{x \left(1 - \sqrt{1 - 4 y}\right)^{3}}{2 y^{3}} + 1}\right)^{2}}{x^{2} \left(1 - \sqrt{1 - 4 y}\right)^{6}}$$
Explicit formula
$$T_{1164}(n, m, k) = \frac{6 k n {\binom{2 k + 2 n - 1}{n}} {\binom{2 m + 3 n - 1}{m}}}{\left(2 k + n\right) \left(m + 3 n\right)}$$
nan | 0 | 0 | 0 | 0 | 0 | 0 |
2 | 6 | 18 | 56 | 18 | 594 | 2002 |
5 | 3 | 135 | 55 | 2145 | 819 | 3094 |
14 | 126 | 756 | 3822 | 1764 | 77112 | 325584 |
42 | 504 | 378 | 22848 | 122094 | 603288 | 2826516 |
132 | 198 | 1782 | 1254 | 7623 | 4207896 | 217074 |
429 | 7722 | 81081 | 651222 | 444015 | 2710422 | 152837685 |
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