Generating function
$$U_{1295}(x, y) = \sqrt{\frac{2 x \left(1 - \sqrt{1 - 4 y}\right)}{y} + 1}$$
Explicit formula
$$Tsqrt(n, k) = \begin{cases}\binom{m}{n} 4^{n}&\text{if k even, where m =} \frac{k} {2},\\\frac {{(-1)}^{n-m} \binom{n}{m} \binom{2n}{n}} {\binom{2n}{2m}} &\text{if k odd, n > m, where m =} \frac{k+1} {2},\\\frac {\binom{2m}{2n} \binom{2n}{n}} {\binom{m}{n}}&\text{if k odd, n} \le \text{m, where m =} \frac{k+1} {2},\\\end{cases} $$$$T_{1295}(n, m, k) = \frac{n \operatorname{Tsqrt}{\left(n,k \right)} {\binom{2 m + n - 1}{m}}}{m + n}$$
nan | 0 | 0 | 0 | 0 | 0 | 0 |
2 | 2 | 4 | 1 | 28 | 84 | 264 |
-2 | -4 | -10 | -28 | -84 | -264 | -858 |
4 | 12 | 36 | 112 | 360 | 1188 | 4004 |
-10 | -40 | -140 | -480 | -1650 | -5720 | -20020 |
28 | 140 | 560 | 2100 | 7700 | 28028 | 101920 |
-84 | -504 | -2268 | -9240 | -36036 | -137592 | -519792 |
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