Generating function
$$U_{64}(x, y) = \frac{- x + \sqrt{x^{2} + 2 y \sqrt{1 - 4 x} + y \left(4 x - 2\right)}}{y \left(\sqrt{1 - 4 x} - 1\right)}$$
Explicit formula
$$T_{64}(n, m, k) = \frac{k {\binom{k + 2 m}{m}} {\binom{k + 2 m + 2 n - 1}{n}}}{k + 2 m + n}$$
1 | 1 | 2 | 5 | 14 | 42 | 132 |
1 | 3 | 1 | 35 | 126 | 462 | 1716 |
2 | 9 | 4 | 175 | 756 | 3234 | 13728 |
5 | 28 | 15 | 77 | 3822 | 1848 | 87516 |
14 | 9 | 55 | 3185 | 1764 | 94248 | 48906 |
42 | 297 | 2002 | 1274 | 77112 | 447678 | 2510508 |
132 | 1001 | 728 | 4998 | 325584 | 2027718 | 12156144 |
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