Generating function
$$U_{927}(x, y) = \frac{i x + i}{\sqrt{4 x y + 4 y - 1}}$$
Explicit formula
$$Tsqrt2(n, k) = \begin{cases}\frac {k \binom{n+j}{n} \binom{2n+2j}{n+j}} {\binom{2j}{j} {n+k}} &\text{if n+k even, where j =} \frac{n+k} {2},\\\frac {k \binom{n+j}{n} \binom{2n+2j}{n+j}} {\binom{2j}{j} {n+k}} &\text{if n+k odd, where j =} \frac{n+k+1} {2},\\\end{cases} $$$$T_{927}(n, m, k) = \frac{k \operatorname{Tsqrt_{2}}{\left(m,k + m \right)} {\binom{k + m}{n}}}{k + m}$$
| 1 | 2 | 6 | 20 | 70 | 252 | 924 |
| 1 | 4 | 18 | 80 | 350 | 1512 | 6468 |
| 0 | 2 | 18 | 120 | 700 | 3780 | 19404 |
| 0 | 0 | 6 | 80 | 700 | 5040 | 32340 |
| 0 | 0 | 0 | 20 | 350 | 3780 | 32340 |
| 0 | 0 | 0 | 0 | 70 | 1512 | 19404 |
| 0 | 0 | 0 | 0 | 0 | 252 | 6468 |
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