Pyramid #930
Generating function
$$U_{930}(x, y) = \frac{1 - \sqrt{- 8 x y - 4 x \sqrt{4 y^{2} + 1} + 1}}{2 x}$$
Explicit formula
$$Tsqrt2(n, k) = \begin{cases}\frac {k \binom{n+j}{n} \binom{2n+2j}{n+j}} {\binom{2j}{j} {n+k}} &\text{if n+k even, where j =} \frac{n+k} {2},\\\frac {k \binom{n+j}{n} \binom{2n+2j}{n+j}} {\binom{2j}{j} {n+k}} &\text{if n+k odd, where j =} \frac{n+k+1} {2},\\\end{cases} $$$$T_{930}(n, m, k) = \frac{k \operatorname{Tsqrt_{2}}{\left(m,k + n \right)} {\binom{k + 2 n - 1}{n}}}{k + n}$$
Data table
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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