Generating function
$$U_{759}(x, y) = \frac{\left(1 - y\right)^{4} \left(1 - \sqrt{- \frac{4 x}{\left(1 - y\right)^{2}} + 1}\right)^{3}}{8 x^{3}}$$
Explicit formula
$$T_{759}(n, m, k) = \frac{3 k {\binom{3 k + 2 n}{n}} {\binom{2 k + m + 2 n - 1}{m}}}{3 k + 2 n}$$
1 | 2 | 3 | 4 | 5 | 6 | 7 |
3 | 12 | 3 | 6 | 105 | 168 | 252 |
9 | 54 | 189 | 504 | 1134 | 2268 | 4158 |
28 | 224 | 1008 | 336 | 924 | 22176 | 48048 |
9 | 9 | 495 | 198 | 6435 | 18018 | 45045 |
297 | 3564 | 23166 | 108108 | 405405 | 1297296 | 3675672 |
1001 | 14014 | 105105 | 56056 | 238238 | 8576568 | 27159132 |
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