Generating function
$$U_{1350}(x, y) = \frac{1 - \sqrt{- 4 x \left(y + 1\right)^{4} + 1}}{2 x \left(y + 1\right)^{4}}$$
Explicit formula
$$T_{1350}(n, m, k) = \frac{k {\binom{4 n}{m}} {\binom{k + 2 n - 1}{n}}}{k + n}$$
1 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 4 | 6 | 4 | 1 | 0 | 0 |
2 | 16 | 56 | 112 | 14 | 112 | 56 |
5 | 6 | 33 | 11 | 2475 | 396 | 462 |
14 | 224 | 168 | 784 | 2548 | 61152 | 112112 |
42 | 84 | 798 | 4788 | 20349 | 651168 | 162792 |
132 | 3168 | 36432 | 267168 | 1402632 | 5610528 | 17766672 |
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