Generating function
$$U_{1386}(x, y) = \frac{1}{\sqrt{1 - 4 x} \left(1 - y\right)^{3}}$$
Explicit formula
$$T_{1386}(n, m, k) = \begin{cases}1&\text{if n=0 , m=0 , k=0} ,\ \\4^{n} {\binom{\frac{k}{2} + n - 1}{n}} {\binom{3 k + m - 1}{m}}&\text{if k even} ,\ \\\frac{{\binom{\frac{k}{2} + n - \frac{1}{2}}{n}} {\binom{k + 2 n - 1}{\frac{k}{2} + n - \frac{1}{2}}} {\binom{3 k + m - 1}{m}}}{{\binom{k - 1}{\frac{k}{2} - \frac{1}{2}}}}&\text{if k odd} \end{cases} $$
1 | 3 | 6 | 1 | 15 | 21 | 28 |
2 | 6 | 12 | 2 | 3 | 42 | 56 |
6 | 18 | 36 | 6 | 9 | 126 | 168 |
2 | 6 | 12 | 2 | 3 | 42 | 56 |
7 | 21 | 42 | 7 | 105 | 147 | 196 |
252 | 756 | 1512 | 252 | 378 | 5292 | 7056 |
924 | 2772 | 5544 | 924 | 1386 | 19404 | 25872 |
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