Generating function
$$U_{1295}(x, y) = \sqrt{\frac{2 x \left(1 - \sqrt{1 - 4 y}\right)}{y} + 1}$$
Explicit formula
$$Tsqrt(n, k) = \begin{cases}\binom{m}{n} 4^{n}&\text{if k even, where m =} \frac{k} {2},\\\frac {{(-1)}^{n-m} \binom{n}{m} \binom{2n}{n}} {\binom{2n}{2m}} &\text{if k odd, n > m, where m =} \frac{k+1} {2},\\\frac {\binom{2m}{2n} \binom{2n}{n}} {\binom{m}{n}}&\text{if k odd, n} \le \text{m, where m =} \frac{k+1} {2},\\\end{cases} $$$$T_{1295}(n, m, k) = \frac{n \operatorname{Tsqrt}{\left(n,k \right)} {\binom{2 m + n - 1}{m}}}{m + n}$$
Data table
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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