Generating function
$$U_{737}(x, y) = \frac{- 2 x \left(y + 1\right)^{4} - \sqrt{- 4 x \left(y + 1\right)^{4} + 1} + 1}{2 x^{2} \left(y + 1\right)^{6}}$$
Explicit formula
$$T_{737}(n, m, k) = \frac{k {\binom{2 k + 2 n}{n}} {\binom{2 k + 4 n}{m}}}{k + n}$$
1 | 2 | 1 | 0 | 0 | 0 | 0 |
2 | 12 | 3 | 4 | 3 | 12 | 2 |
5 | 5 | 225 | 6 | 105 | 126 | 105 |
14 | 196 | 1274 | 5096 | 14014 | 28028 | 42042 |
42 | 756 | 6426 | 34272 | 12852 | 359856 | 779688 |
132 | 2904 | 30492 | 20328 | 96558 | 3476088 | 9848916 |
429 | 11154 | 139425 | 11154 | 641355 | 2821962 | 9876867 |
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