Generating function
$$U_{79}(x, y) = \frac{x^{2}}{2} + x + \frac{\left(x + 1\right) \sqrt{x^{2} + 2 x + 4 y + 1}}{2} + \frac{1}{2}$$
Explicit formula
$$T_{79}(n, m, k) = \begin{cases}1&\text{if n=0 and m=0} ,\ \\\frac{\left(-1\right)^{m - 1} k {\binom{- k + 2 m - 1}{m - 1}}}{m}&\text{if n=0 and m>0} ,\ \\\frac{2 k {\binom{k - m}{m}} {\binom{2 k - 2 m - 1}{n - 1}}}{n}&\text{if n>0} \end{cases} $$
1 | 1 | -1 | 2 | -5 | 14 | -42 |
2 | 0 | 2 | -8 | 3 | -112 | 42 |
1 | 0 | -3 | 2 | -105 | 504 | -231 |
0 | 0 | 4 | -4 | 28 | -168 | 924 |
0 | 0 | -5 | 7 | -63 | 462 | -3003 |
0 | 0 | 6 | -112 | 126 | -11088 | 84084 |
0 | 0 | -7 | 168 | -231 | 24024 | -21021 |
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