Generating function
$$U_{1055}(x, y) = \frac{1}{\sqrt{- 4 x \left(y + 1\right) + 1}}$$
Explicit formula
$$Tsqrt(n, k) = \begin{cases}\binom{m}{n} 4^{n}&\text{if k even, where m =} \frac{k} {2},\\\frac {{(-1)}^{n-m} \binom{n}{m} \binom{2n}{n}} {\binom{2n}{2m}} &\text{if k odd, n > m, where m =} \frac{k+1} {2},\\\frac {\binom{2m}{2n} \binom{2n}{n}} {\binom{m}{n}}&\text{if k odd, n} \le \text{m, where m =} \frac{k+1} {2},\\\end{cases} $$$$T_{1055}(n, m, k) = \frac{k \operatorname{Tsqrt}{\left(n,k + 2 n \right)} {\binom{n}{m}}}{k + 2 n}$$
Data table
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
Export
expand_less