Generating function
$$U_{1387}(x, y) = \frac{1}{\left(1 - y\right)^{2} \sqrt{- \frac{4 x}{\left(1 - y\right)^{2}} + 1}}$$
Explicit formula
$$T_{1387}(n, m, k) = \begin{cases}1&\text{if n=0 , m=0 , k=0} ,\ \\4^{n} {\binom{\frac{k}{2} + n - 1}{n}} {\binom{2 k + m + 2 n - 1}{m}}&\text{if k even} ,\ \\\frac{{\binom{\frac{k}{2} + n - \frac{1}{2}}{n}} {\binom{k + 2 n - 1}{\frac{k}{2} + n - \frac{1}{2}}} {\binom{2 k + m + 2 n - 1}{m}}}{{\binom{k - 1}{\frac{k}{2} - \frac{1}{2}}}}&\text{if k odd} \end{cases} $$
1 | 2 | 3 | 4 | 5 | 6 | 7 |
2 | 8 | 2 | 4 | 7 | 112 | 168 |
6 | 36 | 126 | 336 | 756 | 1512 | 2772 |
2 | 16 | 72 | 24 | 66 | 1584 | 3432 |
7 | 7 | 385 | 154 | 5005 | 14014 | 35035 |
252 | 3024 | 19656 | 91728 | 34398 | 1100736 | 3118752 |
924 | 12936 | 9702 | 51744 | 219912 | 7916832 | 25069968 |
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