Pyramid #336
Generating function
$$U_{336}(x, y) = \frac{- \sqrt{2 x \left(\sqrt{4 y + 1} + 1\right) + \frac{\left(\sqrt{4 y + 1} + 1\right)^{4}}{16}} + \frac{\left(\sqrt{4 y + 1} + 1\right)^{2}}{4}}{\sqrt{4 y + 1} + 1}$$
Explicit formula
$$T_{336}(n, m, k) = \begin{cases}0&\text{if n<k} ,\ \\- \frac{\left(-1\right)^{n - 1} k {\binom{- k + 2 n - 1}{n - 1}}}{n}&\text{if m=0} ,\ \\- \frac{\left(-1\right)^{m - 1} k \left(k - 3 n\right) {\binom{k - n - 1}{n - 1}} {\binom{- k + 2 m + 3 n - 1}{m - 1}}}{m n}&\text{if m>0} \end{cases} $$
Data table
0 0 0 0 0 0 0
-1 2 -5 14 -42 132 -429
1 -5 2 -75 275 -1001 364
-2 16 -88 416 -182 7616 -31008
5 -55 385 -22 1122 -53295 241395
-14 196 -1666 11172 -6517 347116 -173558
42 -714 714 -54978 361284 -213486 1169532
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