Pyramid #320
Generating function
$$U_{320}(x, y) = \frac{1 - \sqrt{4 x y^{6} - 24 x y^{5} + 60 x y^{4} - 80 x y^{3} + 60 x y^{2} - 24 x y + 4 x + 1}}{2 y^{2} - 4 y + 2}$$
Explicit formula
$$T_{320}(n, m, k) = \begin{cases}0&\text{if n<k} ,\ \\- \frac{k {\binom{k - n - 1}{n - 1}} {\binom{2 k + m - 6 n - 1}{m}}}{n} \end{cases} $$
Data table
0 0 0 0 0 0 0
-1 4 -6 4 -1 0 0
1 -1 45 -12 21 -252 21
-2 32 -24 112 -364 8736 -16016
5 -11 1155 -77 36575 -13167 373065
-14 392 -5292 45864 -28665 137592 -527436
42 -1428 23562 -251328 1947792 -11686752 56485968
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