Generating function
$$U_{716}(x, y) = \sqrt{\frac{4 x + 1}{1 - 4 y}}$$
Explicit formula
$$TA_{984}(n, k) = \begin{cases}{4}^{n} \binom {n+j-1} {n} &\text{if k even, where j =} \frac {k} {2},\\\frac {\binom {n+j} {n} \binom {2n+2j} {n+j}} {\binom {2j} {j}}&\text{if k odd, where j =} \frac {k-1} {2},\end{cases} $$$$Tsqrt(n, k) = \begin{cases}\binom{m}{n} 4^{n}&\text{if k even, where m =} \frac{k} {2},\\\frac {{(-1)}^{n-m} \binom{n}{m} \binom{2n}{n}} {\binom{2n}{2m}} &\text{if k odd, n > m, where m =} \frac{k+1} {2},\\\frac {\binom{2m}{2n} \binom{2n}{n}} {\binom{m}{n}}&\text{if k odd, n} \le \text{m, where m =} \frac{k+1} {2},\\\end{cases} $$$$T_{716}(n, m, k) = \operatorname{TA_{984}}{\left(m,k \right)} \operatorname{Tsqrt}{\left(n,k \right)}$$
1 | 2 | 6 | 20 | 70 | 252 | 924 |
2 | 4 | 12 | 40 | 140 | 504 | 1848 |
-2 | -4 | -12 | -40 | -140 | -504 | -1848 |
4 | 8 | 24 | 80 | 280 | 1008 | 3696 |
-10 | -20 | -60 | -200 | -700 | -2520 | -9240 |
28 | 56 | 168 | 560 | 1960 | 7056 | 25872 |
-84 | -168 | -504 | -1680 | -5880 | -21168 | -77616 |
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