Generating function
$$U_{848}(x, y) = \frac{1 - \sqrt{- \frac{4 x}{1 - y} + 1}}{2 x \left(1 - y\right)^{3}}$$
Explicit formula
$$T_{848}(n, m, k) = \frac{k {\binom{k + 2 n - 1}{n}} {\binom{4 k + m + n - 1}{m}}}{k + n}$$
1 | 4 | 1 | 2 | 35 | 56 | 84 |
1 | 5 | 15 | 35 | 7 | 126 | 21 |
2 | 12 | 42 | 112 | 252 | 504 | 924 |
5 | 35 | 14 | 42 | 105 | 231 | 462 |
14 | 112 | 504 | 168 | 462 | 11088 | 24024 |
42 | 378 | 189 | 693 | 2079 | 54054 | 126126 |
132 | 132 | 726 | 2904 | 9438 | 264264 | 66066 |
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