Generating function
$$U_{1336}(x, y) = \frac{2 \sqrt{3} \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{x} \left(y + 1\right)^{5}}{2} \right)}}{3} \right)}}{3 \sqrt{x}}$$
Explicit formula
$$T_{1336}(n, m, k) = \frac{k {\binom{k + 3 n}{n}} {\binom{5 k + 10 n}{m}}}{k + 3 n}$$
1 | 5 | 1 | 1 | 5 | 1 | 0 |
1 | 15 | 105 | 455 | 1365 | 3003 | 5005 |
3 | 75 | 9 | 69 | 3795 | 15939 | 5313 |
12 | 42 | 714 | 7854 | 62832 | 3895584 | 1947792 |
55 | 2475 | 5445 | 78045 | 8194725 | 67196745 | 4479783 |
273 | 15015 | 405405 | 7162155 | 93108015 | 949701753 | 7914181275 |
1428 | 9282 | 297024 | 6237504 | 96681312 | 11795120064 | 11795120064 |
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