Generating function
$$U_{1305}(x, y) = \frac{\left(1 - y\right)^{9} \left(- \frac{2 x}{\left(1 - y\right)^{3}} - \sqrt{- \frac{4 x}{\left(1 - y\right)^{3}} + 1} + 1\right)^{2}}{4 x^{4}}$$
Explicit formula
$$T_{1305}(n, m, k) = \frac{2 k {\binom{4 k + 2 n}{n}} {\binom{3 k + m + 3 n - 1}{m}}}{2 k + n}$$
1 | 3 | 6 | 1 | 15 | 21 | 28 |
4 | 24 | 84 | 224 | 504 | 1008 | 1848 |
14 | 126 | 63 | 231 | 693 | 18018 | 42042 |
48 | 576 | 3744 | 17472 | 6552 | 209664 | 594048 |
165 | 2475 | 198 | 1122 | 5049 | 191862 | 63954 |
572 | 10296 | 97812 | 65208 | 342342 | 15063048 | 57741684 |
2002 | 42042 | 462462 | 3545542 | 21273252 | 10636626 | 46092046 |
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