Generating function
$$U_{139}(x, y) = \frac{- 2 x - y - \sqrt{- 4 x + y^{2} - y \left(2 - 4 x\right) + 1} + 1}{2 x^{2}}$$
Explicit formula
$$T_{139}(n, m, k) = \begin{cases}\frac{k {\binom{k + 2 m - 1}{m}}}{k + m}&\text{if n=0} ,\ \\\frac{k {\binom{2 k + 2 n}{n}} {\binom{k + m + n}{m}}}{k + m + n} \end{cases} $$
1 | 1 | 2 | 5 | 14 | 42 | 132 |
2 | 4 | 6 | 8 | 1 | 12 | 14 |
5 | 15 | 3 | 5 | 75 | 105 | 14 |
14 | 56 | 14 | 28 | 49 | 784 | 1176 |
42 | 21 | 63 | 147 | 294 | 5292 | 882 |
132 | 792 | 2772 | 7392 | 16632 | 33264 | 60984 |
429 | 3003 | 12012 | 36036 | 9009 | 198198 | 396396 |
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