Generating function
$$U_{1285}(x, y) = \frac{\sqrt{4 x + 1}}{\left(1 - y\right)^{3}}$$
Explicit formula
$$Tsqrt(n, k) = \begin{cases}\binom{m}{n} 4^{n}&\text{if k even, where m =} \frac{k} {2},\\\frac {{(-1)}^{n-m} \binom{n}{m} \binom{2n}{n}} {\binom{2n}{2m}} &\text{if k odd, n > m, where m =} \frac{k+1} {2},\\\frac {\binom{2m}{2n} \binom{2n}{n}} {\binom{m}{n}}&\text{if k odd, n} \le \text{m, where m =} \frac{k+1} {2},\\\end{cases} $$$$T_{1285}(n, m, k) = k \operatorname{Tsqrt}{\left(n,k \right)} {\binom{3 k + m - 1}{m}}$$
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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