Generating function
$$U_{1458}(x, y) = \frac{\left(1 - y\right)^{5} \left(- \frac{2 x}{\left(1 - y\right)^{3}} - \sqrt{- \frac{4 x}{\left(1 - y\right)^{3}} + 1} + 1\right)}{2 x^{2}}$$
Explicit formula
$$T_{1458}(n, m, k) = \frac{k {\binom{2 k + 2 n}{n}} {\binom{k + m + 3 n - 1}{m}}}{k + n}$$
1 | 1 | 1 | 1 | 1 | 1 | 1 |
2 | 8 | 2 | 4 | 7 | 112 | 168 |
5 | 35 | 14 | 42 | 105 | 231 | 462 |
14 | 14 | 77 | 308 | 1001 | 28028 | 7007 |
42 | 546 | 3822 | 1911 | 7644 | 259896 | 779688 |
132 | 2112 | 17952 | 107712 | 511632 | 2046528 | 7162848 |
429 | 8151 | 8151 | 57057 | 3138135 | 14435421 | 57741684 |
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