Pyramid 309

Pyramid #308

Pyramid #309

Pyramid #310

Generating function

$$U_{309}(x, y) = \frac{- 2 x y^{2} + 2 y + \sqrt{1 - 4 y} - 1}{y \left(\sqrt{1 - 4 y} - 1\right)}$$

Explicit formula

$$T_{309}(n, m, k) = \begin{cases}{\binom{k}{n}}&\text{if m=0} ,\ \\\frac{\left(-1\right)^{m - 1} \left(k - 2 n\right) {\binom{k}{n}} {\binom{- k - m + 2 n - 1}{m - 1}}}{m} \end{cases} $$

Data table
1	1	2	5	14	42	132
1	-1	-1	-2	-5	-14	-42
0	0	0	0	0	0	0
0	0	0	0	0	0	0
0	0	0	0	0	0	0
0	0	0	0	0	0	0
0	0	0	0	0	0	0

Pyramid #308: Right on x

Export

1	1	2	5	14	42	132
1	-1	-1	-2	-5	-14	-42
0	0	0	0	0	0	0
0	0	0	0	0	0	0
0	0	0	0	0	0	0
0	0	0	0	0	0	0
0	0	0	0	0	0	0

1	1	2	5	14	42	132
1	-1	-1	-2	-5	-14	-42
0	0	0	0	0	0	0
0	0	0	0	0	0	0
0	0	0	0	0	0	0
0	0	0	0	0	0	0
0	0	0	0	0	0	0

1	1	2	5	14	42	132
1	-1	-1	-2	-5	-14	-42
0	0	0	0	0	0	0
0	0	0	0	0	0	0
0	0	0	0	0	0	0
0	0	0	0	0	0	0
0	0	0	0	0	0	0