Generating function
$$U_{1268}(x, y) = \frac{1 - \sqrt{- \frac{x \left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{2}}{y^{4}} + 1}}{2 x}$$
Explicit formula
$$T_{1268}(n, m, k) = \frac{2 k {\binom{k + 2 n - 1}{n}} {\binom{4 k + 2 m + 4 n}{m}}}{2 k + m + 2 n}$$
1 | 4 | 14 | 48 | 165 | 572 | 2002 |
1 | 8 | 44 | 208 | 91 | 3808 | 15504 |
2 | 24 | 18 | 1088 | 5814 | 28728 | 134596 |
5 | 8 | 76 | 56 | 3542 | 2024 | 10764 |
14 | 28 | 322 | 28 | 20475 | 1330056 | 792918 |
42 | 1008 | 13608 | 136416 | 113274 | 8249472 | 54538176 |
132 | 3696 | 57288 | 650496 | 604758 | 48820464 | 354666312 |
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