Generating function
$$U_{941}(x, y) = 2 x y + \sqrt{4 x^{2} y^{2} + 4 x + 1}$$
Explicit formula
$$Tsqrt(n, k) = \begin{cases}\binom{m}{n} 4^{n}&\text{if k even, where m =} \frac{k} {2},\\\frac {{(-1)}^{n-m} \binom{n}{m} \binom{2n}{n}} {\binom{2n}{2m}} &\text{if k odd, n > m, where m =} \frac{k+1} {2},\\\frac {\binom{2m}{2n} \binom{2n}{n}} {\binom{m}{n}}&\text{if k odd, n} \le \text{m, where m =} \frac{k+1} {2},\\\end{cases} $$$$T_{941}(n, m, k) = \frac{k \operatorname{Tsqrt}{\left(n,k + m \right)} {\binom{n}{m}}}{k + m}$$
1 | 0 | 0 | 0 | 0 | 0 | 0 |
2 | 2 | 0 | 0 | 0 | 0 | 0 |
-2 | 0 | 2 | 0 | 0 | 0 | 0 |
4 | 0 | -4 | 0 | 0 | 0 | 0 |
-10 | 0 | 12 | 0 | -2 | 0 | 0 |
28 | 0 | -40 | 0 | 12 | 0 | 0 |
-84 | 0 | 140 | 0 | -60 | 0 | 4 |
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