Pyramid #738
Generating function
$$U_{738}(x, y) = \frac{\left(1 - \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{- x}}{2} \right)}}{3} \right)}}{3}\right)^{2}}{\left(1 - y\right)^{2}}$$
Explicit formula
$$T_{738}(n, m, k) = \begin{cases}{\binom{2 k + m - 1}{m}}&\text{if n=0} ,\ \\\frac{2 \left(-1\right)^{n - 1} k {\binom{- 2 k + 3 n - 1}{n - 1}} {\binom{2 k + m - 1}{m}}}{n}&\text{if n>0} \end{cases} $$
Data table
1 2 3 4 5 6 7
2 4 6 8 1 12 14
-3 -6 -9 -12 -15 -18 -21
1 2 3 4 5 6 7
-42 -84 -126 -168 -21 -252 -294
198 396 594 792 99 1188 1386
-1001 -2002 -3003 -4004 -5005 -6006 -7007
Export
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