Generating function
$$U_{846}(x, y) = \frac{1 - \sqrt{- \frac{4 x}{1 - y} + 1}}{2 x \left(1 - y\right)^{2}}$$
Explicit formula
$$T_{846}(n, m, k) = \frac{k {\binom{k + 2 n - 1}{n}} {\binom{3 k + m + n - 1}{m}}}{k + n}$$
1 | 3 | 6 | 1 | 15 | 21 | 28 |
1 | 4 | 1 | 2 | 35 | 56 | 84 |
2 | 1 | 3 | 7 | 14 | 252 | 42 |
5 | 3 | 105 | 28 | 63 | 126 | 231 |
14 | 98 | 392 | 1176 | 294 | 6468 | 12936 |
42 | 336 | 1512 | 504 | 1386 | 33264 | 72072 |
132 | 1188 | 594 | 2178 | 6534 | 169884 | 396396 |
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