Pyramid #925
Generating function
$$U_{925}(x, y) = \frac{- 2 y - \sqrt{4 y^{2} + 1}}{2 x y + x \sqrt{4 y^{2} + 1} - 1}$$
Explicit formula
$$Tsqrt2(n, k) = \begin{cases}\frac {k \binom{n+j}{n} \binom{2n+2j}{n+j}} {\binom{2j}{j} {n+k}} &\text{if n+k even, where j =} \frac{n+k} {2},\\\frac {k \binom{n+j}{n} \binom{2n+2j}{n+j}} {\binom{2j}{j} {n+k}} &\text{if n+k odd, where j =} \frac{n+k+1} {2},\\\end{cases} $$$$T_{925}(n, m, k) = \frac{k \operatorname{Tsqrt_{2}}{\left(m,k + n \right)} {\binom{k + n}{n}}}{k + n}$$
Data table
1 2 2 0 -2 0 4
1 4 8 8 0 -8 0
1 6 18 32 30 0 -28
1 8 32 80 128 112 0
1 10 50 160 350 512 420
1 12 72 280 768 1512 2048
1 14 98 448 1470 3584 6468
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