Generating function
$$U_{1325}(x, y) = \frac{- x - 2 y - \sqrt{x^{2} - 2 x - 4 y + 1} + 1}{2 x y + 2 y^{2}}$$
Explicit formula
$$T_{1325}(n, m, k) = \frac{k {\binom{2 k + 2 m + n}{m}} {\binom{k + m + n - 1}{n}}}{k + m}$$
1 | 2 | 5 | 14 | 42 | 132 | 429 |
1 | 5 | 21 | 84 | 33 | 1287 | 5005 |
1 | 9 | 56 | 3 | 1485 | 7007 | 32032 |
1 | 14 | 12 | 825 | 5005 | 28028 | 148512 |
1 | 2 | 225 | 1925 | 14014 | 91728 | 55692 |
1 | 27 | 385 | 4004 | 34398 | 259896 | 1790712 |
1 | 35 | 616 | 7644 | 7644 | 659736 | 511632 |
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