Generating function
$$U_{1386}(x, y) = \frac{1}{\sqrt{1 - 4 x} \left(1 - y\right)^{3}}$$
Explicit formula
$$T_{1386}(n, m, k) = \begin{cases}1&\text{if n=0 , m=0 , k=0} ,\ \\4^{n} {\binom{\frac{k}{2} + n - 1}{n}} {\binom{3 k + m - 1}{m}}&\text{if k even} ,\ \\\frac{{\binom{\frac{k}{2} + n - \frac{1}{2}}{n}} {\binom{k + 2 n - 1}{\frac{k}{2} + n - \frac{1}{2}}} {\binom{3 k + m - 1}{m}}}{{\binom{k - 1}{\frac{k}{2} - \frac{1}{2}}}}&\text{if k odd} \end{cases} $$
Data table
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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