Generating function
$$U_{749}(x, y) = \frac{y^{3} \left(- \frac{2 x \left(1 - \sqrt{1 - 4 y}\right)^{2}}{y^{2}} - 4 \sqrt{- \frac{x \left(1 - \sqrt{1 - 4 y}\right)^{2}}{y^{2}} + 1} + 4\right)}{x^{2} \left(1 - \sqrt{1 - 4 y}\right)^{3}}$$
Explicit formula
$$T_{749}(n, m, k) = \frac{k \left(k + 2 n\right) {\binom{2 k + 2 n}{n}} {\binom{k + 2 m + 2 n - 1}{m}}}{\left(k + n\right) \left(k + m + 2 n\right)}$$
1 | 1 | 2 | 5 | 14 | 42 | 132 |
2 | 6 | 18 | 56 | 18 | 594 | 2002 |
5 | 25 | 1 | 375 | 1375 | 5005 | 182 |
14 | 98 | 49 | 2156 | 8918 | 35672 | 139944 |
42 | 378 | 2268 | 11466 | 5292 | 231336 | 976752 |
132 | 1452 | 10164 | 5808 | 296208 | 1406988 | 6372828 |
429 | 5577 | 44616 | 284427 | 1589445 | 8159151 | 39507468 |
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