Generating function
$$U_{1361}(x, y) = \frac{\left(1 - \sqrt{1 - 4 y}\right)^{2} \sqrt{\frac{x \left(1 - \sqrt{1 - 4 y}\right)^{3}}{2 y^{3}} + 1}}{4 y^{2}}$$
Explicit formula
$$Tsqrt(n, k) = \begin{cases}\binom{m}{n} 4^{n}&\text{if k even, where m =} \frac{k} {2},\\\frac {{(-1)}^{n-m} \binom{n}{m} \binom{2n}{n}} {\binom{2n}{2m}} &\text{if k odd, n > m, where m =} \frac{k+1} {2},\\\frac {\binom{2m}{2n} \binom{2n}{n}} {\binom{m}{n}}&\text{if k odd, n} \le \text{m, where m =} \frac{k+1} {2},\\\end{cases} $$$$T_{1361}(n, m, k) = \frac{\left(2 k + 3 n\right) \operatorname{Tsqrt}{\left(n,k \right)} {\binom{2 k + 2 m + 3 n - 1}{m}}}{2 k + m + 3 n}$$
1 | 2 | 5 | 14 | 42 | 132 | 429 |
2 | 1 | 4 | 15 | 55 | 2002 | 728 |
-2 | -16 | -88 | -416 | -1820 | -7616 | -31008 |
4 | 44 | 308 | 1760 | 8976 | 42636 | 193116 |
-10 | -140 | -1190 | -7980 | -46550 | -247940 | -1239700 |
28 | 476 | 4760 | 36652 | 240856 | 1423240 | 7796880 |
-84 | -1680 | -19320 | -168000 | -1228500 | -7980336 | -47575080 |
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