Generating function
$$U_{1454}(x, y) = \frac{- \frac{2 x}{1 - y} - \sqrt{- \frac{4 x}{1 - y} + 1} + 1}{2 x^{2}}$$
Explicit formula
$$T_{1454}(n, m, k) = \frac{k {\binom{2 k + 2 n}{n}} {\binom{2 k + m + n - 1}{m}}}{k + n}$$
1 | 2 | 3 | 4 | 5 | 6 | 7 |
2 | 6 | 12 | 2 | 3 | 42 | 56 |
5 | 2 | 5 | 1 | 175 | 28 | 42 |
14 | 7 | 21 | 49 | 98 | 1764 | 294 |
42 | 252 | 882 | 2352 | 5292 | 10584 | 19404 |
132 | 924 | 3696 | 11088 | 2772 | 60984 | 121968 |
429 | 3432 | 15444 | 5148 | 14157 | 339768 | 736164 |
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