Pyramid #935
Generating function
$$U_{935}(x, y) = \frac{2 x y - x \sqrt{- 4 x y + 4 y^{2} + 1} - 1}{4 x y - 1}$$
Explicit formula
$$Tsqrt2(n, k) = \begin{cases}\frac {k \binom{n+j}{n} \binom{2n+2j}{n+j}} {\binom{2j}{j} {n+k}} &\text{if n+k even, where j =} \frac{n+k} {2},\\\frac {k \binom{n+j}{n} \binom{2n+2j}{n+j}} {\binom{2j}{j} {n+k}} &\text{if n+k odd, where j =} \frac{n+k+1} {2},\\\end{cases} $$$$T_{935}(n, m, k) = \begin{cases}1&\text{if n=0 , m=0} ,\ \\\frac{k \operatorname{Tsqrt_{2}}{\left(m,n \right)} {\binom{k + m}{n}}}{k + m} \end{cases} $$
Data table
1 0 0 0 0 0 0
1 2 2 0 -2 0 4
0 2 8 12 0 -20 0
0 0 6 32 60 0 -140
0 0 0 20 128 280 0
0 0 0 0 70 512 1260
0 0 0 0 0 252 2048
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