Generating function
$$U_{1358}(x, y) = \frac{2 \sqrt{3} \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{x} \left(- 2 y - \sqrt{1 - 4 y} + 1\right)}{4 y^{2}} \right)}}{3} \right)}}{3 \sqrt{x}}$$
Explicit formula
$$T_{1358}(n, m, k) = \frac{k {\binom{k + 3 n - 1}{n}} {\binom{2 k + 2 m + 4 n}{m}}}{k + m + 2 n}$$
1 | 2 | 5 | 14 | 42 | 132 | 429 |
1 | 6 | 27 | 11 | 429 | 1638 | 6188 |
3 | 3 | 195 | 105 | 51 | 23256 | 101745 |
12 | 168 | 1428 | 9576 | 5586 | 297528 | 148764 |
55 | 99 | 10395 | 8349 | 56925 | 34749 | 19594575 |
273 | 6006 | 75075 | 702702 | 5486481 | 37795758 | 237573336 |
1428 | 37128 | 538356 | 575484 | 50642592 | 388804416 | 2697330636 |
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