Generating function
$$U_{1055}(x, y) = \frac{1}{\sqrt{- 4 x \left(y + 1\right) + 1}}$$
Explicit formula
$$Tsqrt(n, k) = \begin{cases}\binom{m}{n} 4^{n}&\text{if k even, where m =} \frac{k} {2},\\\frac {{(-1)}^{n-m} \binom{n}{m} \binom{2n}{n}} {\binom{2n}{2m}} &\text{if k odd, n > m, where m =} \frac{k+1} {2},\\\frac {\binom{2m}{2n} \binom{2n}{n}} {\binom{m}{n}}&\text{if k odd, n} \le \text{m, where m =} \frac{k+1} {2},\\\end{cases} $$$$T_{1055}(n, m, k) = \frac{k \operatorname{Tsqrt}{\left(n,k + 2 n \right)} {\binom{n}{m}}}{k + 2 n}$$
1 | 0 | 0 | 0 | 0 | 0 | 0 |
2 | 2 | 0 | 0 | 0 | 0 | 0 |
6 | 12 | 6 | 0 | 0 | 0 | 0 |
20 | 60 | 60 | 20 | 0 | 0 | 0 |
70 | 280 | 420 | 280 | 70 | 0 | 0 |
252 | 1260 | 2520 | 2520 | 1260 | 252 | 0 |
924 | 5544 | 13860 | 18480 | 13860 | 5544 | 924 |
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