Generating function
$$U_{1285}(x, y) = \frac{\sqrt{4 x + 1}}{\left(1 - y\right)^{3}}$$
Explicit formula
$$Tsqrt(n, k) = \begin{cases}\binom{m}{n} 4^{n}&\text{if k even, where m =} \frac{k} {2},\\\frac {{(-1)}^{n-m} \binom{n}{m} \binom{2n}{n}} {\binom{2n}{2m}} &\text{if k odd, n > m, where m =} \frac{k+1} {2},\\\frac {\binom{2m}{2n} \binom{2n}{n}} {\binom{m}{n}}&\text{if k odd, n} \le \text{m, where m =} \frac{k+1} {2},\\\end{cases} $$$$T_{1285}(n, m, k) = k \operatorname{Tsqrt}{\left(n,k \right)} {\binom{3 k + m - 1}{m}}$$
Data table
1 3 6 1 15 21 28
2 6 12 2 3 42 56
-2 -6 -12 -20 -30 -42 -56
4 12 24 40 60 84 112
-10 -30 -60 -100 -150 -210 -280
28 84 168 280 420 588 784
-84 -252 -504 -840 -1260 -1764 -2352
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