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
$$T_{1336}(n, m, k) = \frac{k {\binom{k + 3 n}{n}} {\binom{5 k + 10 n}{m}}}{k + 3 n}$$
Data table
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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