Generating function
$$U_{1302}(x, y) = \frac{\left(- 2 x \left(y + 1\right)^{3} - \sqrt{- 4 x \left(y + 1\right)^{3} + 1} + 1\right)^{2}}{4 x^{4} \left(y + 1\right)^{9}}$$
Explicit formula
$$T_{1302}(n, m, k) = \frac{2 k {\binom{3 k + 3 n}{m}} {\binom{4 k + 2 n}{n}}}{2 k + n}$$
1 | 3 | 3 | 1 | 0 | 0 | 0 |
4 | 24 | 6 | 8 | 6 | 24 | 4 |
14 | 126 | 504 | 1176 | 1764 | 1764 | 1176 |
48 | 576 | 3168 | 1056 | 2376 | 38016 | 44352 |
165 | 2475 | 17325 | 75075 | 225225 | 495495 | 825825 |
572 | 10296 | 87516 | 466752 | 175032 | 4900896 | 10618608 |
2002 | 42042 | 42042 | 266266 | 1198197 | 40738698 | 108636528 |
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