Generating function
$$U_{760}(x, y) = \frac{y^{2} \left(1 - \sqrt{- \frac{2 x \left(1 - \sqrt{1 - 4 y}\right)}{y} + 1}\right)^{3}}{2 x^{3} \left(1 - \sqrt{1 - 4 y}\right)^{2}}$$
Explicit formula
$$T_{760}(n, m, k) = \frac{3 k \left(k + n\right) {\binom{3 k + 2 n}{n}} {\binom{k + 2 m + n - 1}{m}}}{\left(3 k + 2 n\right) \left(k + m + n\right)}$$
1 | 1 | 2 | 5 | 14 | 42 | 132 |
3 | 6 | 15 | 42 | 126 | 396 | 1287 |
9 | 27 | 81 | 252 | 81 | 2673 | 9009 |
28 | 112 | 392 | 1344 | 462 | 16016 | 56056 |
9 | 45 | 18 | 675 | 2475 | 9009 | 3276 |
297 | 1782 | 8019 | 3267 | 127413 | 486486 | 1837836 |
1001 | 7007 | 35035 | 154154 | 637637 | 2550548 | 10005996 |
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