Generating function
$$U_{1456}(x, y) = \frac{\left(1 - y\right)^{2} \left(- \frac{2 x}{\left(1 - y\right)^{2}} - \sqrt{- \frac{4 x}{\left(1 - y\right)^{2}} + 1} + 1\right)}{2 x^{2}}$$
Explicit formula
$$T_{1456}(n, m, k) = \frac{k {\binom{2 k + 2 n}{n}} {\binom{2 k + m + 2 n - 1}{m}}}{k + n}$$
1 | 2 | 3 | 4 | 5 | 6 | 7 |
2 | 8 | 2 | 4 | 7 | 112 | 168 |
5 | 3 | 105 | 28 | 63 | 126 | 231 |
14 | 112 | 504 | 168 | 462 | 11088 | 24024 |
42 | 42 | 231 | 924 | 3003 | 84084 | 21021 |
132 | 1584 | 10296 | 48048 | 18018 | 576576 | 1633632 |
429 | 6006 | 45045 | 24024 | 102102 | 3675672 | 11639628 |
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