Generating function
$$U_{930}(x, y) = \frac{1 - \sqrt{- 8 x y - 4 x \sqrt{4 y^{2} + 1} + 1}}{2 x}$$
Explicit formula
$$Tsqrt2(n, k) = \begin{cases}\frac {k \binom{n+j}{n} \binom{2n+2j}{n+j}} {\binom{2j}{j} {n+k}} &\text{if n+k even, where j =} \frac{n+k} {2},\\\frac {k \binom{n+j}{n} \binom{2n+2j}{n+j}} {\binom{2j}{j} {n+k}} &\text{if n+k odd, where j =} \frac{n+k+1} {2},\\\end{cases} $$$$T_{930}(n, m, k) = \frac{k \operatorname{Tsqrt_{2}}{\left(m,k + n \right)} {\binom{k + 2 n - 1}{n}}}{k + n}$$
1 | 2 | 2 | 0 | -2 | 0 | 4 |
1 | 4 | 8 | 8 | 0 | -8 | 0 |
2 | 12 | 36 | 64 | 60 | 0 | -56 |
5 | 40 | 160 | 400 | 640 | 560 | 0 |
14 | 140 | 700 | 2240 | 4900 | 7168 | 5880 |
42 | 504 | 3024 | 11760 | 32256 | 63504 | 86016 |
132 | 1848 | 12936 | 59136 | 194040 | 473088 | 853776 |
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