Generating function
$$U_{761}(x, y) = \frac{y^{4} \left(1 - \sqrt{- \frac{2 x \left(- 2 y - \sqrt{1 - 4 y} + 1\right)}{y^{2}} + 1}\right)^{3}}{2 x^{3} \left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{2}}$$
Explicit formula
$$T_{761}(n, m, k) = \frac{3 k \left(k + n\right) {\binom{3 k + 2 n}{n}} {\binom{2 k + 2 m + 2 n}{m}}}{\left(3 k + 2 n\right) \left(k + m + n\right)}$$
1 | 2 | 5 | 14 | 42 | 132 | 429 |
3 | 12 | 42 | 144 | 495 | 1716 | 6006 |
9 | 54 | 243 | 99 | 3861 | 14742 | 55692 |
28 | 224 | 1232 | 5824 | 2548 | 106624 | 434112 |
9 | 9 | 585 | 315 | 153 | 69768 | 305235 |
297 | 3564 | 2673 | 161568 | 863379 | 4266108 | 19987506 |
1001 | 14014 | 119119 | 798798 | 4659655 | 24818794 | 12409397 |
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