Generating function
$$U_{718}(x, y) = \frac{1 - \sqrt{- 4 x \left(4 y + 1\right)^{\frac{3}{2}} + 1}}{2 x \left(4 y + 1\right)}$$
Explicit formula
$$Tsqrt(n, k) = \begin{cases}\binom{m}{n} 4^{n}&\text{if k even, where m =} \frac{k} {2},\\\frac {{(-1)}^{n-m} \binom{n}{m} \binom{2n}{n}} {\binom{2n}{2m}} &\text{if k odd, n > m, where m =} \frac{k+1} {2},\\\frac {\binom{2m}{2n} \binom{2n}{n}} {\binom{m}{n}}&\text{if k odd, n} \le \text{m, where m =} \frac{k+1} {2},\\\end{cases} $$$$T_{718}(n, m, k) = \frac{k \operatorname{Tsqrt}{\left(m,k + 3 n \right)} {\binom{k + 2 n}{n}}}{k + 2 n}$$
1 | 2 | -2 | 4 | -10 | 28 | -84 |
1 | 8 | 16 | 0 | 0 | 0 | 0 |
2 | 28 | 140 | 280 | 14 | -56 | 56 |
5 | 100 | 800 | 3200 | 6400 | 512 | 0 |
14 | 364 | 4004 | 24024 | 84084 | 168168 | 168168 |
42 | 1344 | 18816 | 150528 | 752640 | 2408448 | 4816896 |
132 | 5016 | 85272 | 852720 | 5542680 | 24387792 | 73163376 |
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