Pyramid #926
Generating function
$$U_{926}(x, y) = \frac{1 - \sqrt{- 32 x y^{2} - 16 x y \sqrt{4 y^{2} + 1} - 4 x + 1}}{4 x y + 2 x \sqrt{4 y^{2} + 1}}$$
Explicit formula
$$Tsqrt2(n, k) = \begin{cases}\frac {k \binom{n+j}{n} \binom{2n+2j}{n+j}} {\binom{2j}{j} {n+k}} &\text{if n+k even, where j =} \frac{n+k} {2},\\\frac {k \binom{n+j}{n} \binom{2n+2j}{n+j}} {\binom{2j}{j} {n+k}} &\text{if n+k odd, where j =} \frac{n+k+1} {2},\\\end{cases} $$$$T_{926}(n, m, k) = \frac{k \operatorname{Tsqrt_{2}}{\left(m,k + 2 n \right)} {\binom{k + 2 n}{n}}}{k + 2 n}$$
Data table
1 2 2 0 -2 0 4
1 6 18 32 30 0 -28
2 20 100 320 700 1024 840
5 70 490 2240 7350 17920 32340
14 252 2268 13440 58212 193536 504504
42 924 10164 73920 396396 1655808 5549544
132 3432 44616 384384 2453880 12300288 50059152
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