Generating function
$$U_{758}(x, y) = \frac{\left(1 - \sqrt{- 4 x \left(y + 1\right)^{2} + 1}\right)^{3}}{8 x^{3} \left(y + 1\right)^{4}}$$
Explicit formula
$$T_{758}(n, m, k) = \frac{3 k {\binom{2 k + 2 n}{m}} {\binom{3 k + 2 n}{n}}}{3 k + 2 n}$$
1 | 2 | 1 | 0 | 0 | 0 | 0 |
3 | 12 | 18 | 12 | 3 | 0 | 0 |
9 | 54 | 135 | 18 | 135 | 54 | 9 |
28 | 224 | 784 | 1568 | 196 | 1568 | 784 |
9 | 9 | 405 | 108 | 189 | 2268 | 189 |
297 | 3564 | 19602 | 6534 | 147015 | 235224 | 274428 |
1001 | 14014 | 91091 | 364364 | 1002001 | 2004002 | 3006003 |
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