Generating function
$$U_{740}(x, y) = \frac{\left(1 - y\right)^{6} \left(- \frac{2 x}{\left(1 - y\right)^{4}} - \sqrt{- \frac{4 x}{\left(1 - y\right)^{4}} + 1} + 1\right)}{2 x^{2}}$$
Explicit formula
$$T_{740}(n, m, k) = \frac{k {\binom{2 k + 2 n}{n}} {\binom{2 k + m + 4 n - 1}{m}}}{k + n}$$
1 | 2 | 3 | 4 | 5 | 6 | 7 |
2 | 12 | 42 | 112 | 252 | 504 | 924 |
5 | 5 | 275 | 11 | 3575 | 1001 | 25025 |
14 | 196 | 147 | 784 | 3332 | 119952 | 379848 |
42 | 756 | 7182 | 4788 | 25137 | 1106028 | 4239774 |
132 | 2904 | 33396 | 267168 | 16698 | 868296 | 3907332 |
429 | 11154 | 150579 | 1405404 | 10189179 | 61135074 | 315864549 |
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