Pyramid 334

Pyramid #333

Pyramid #334

Pyramid #335

Generating function

$$U_{334}(x, y) = \frac{2 x + \frac{\left(\sqrt{4 y + 1} + 1\right)^{2}}{2}}{\sqrt{4 y + 1} + 1}$$

Explicit formula

$$T_{334}(n, m, k) = \begin{cases}{\binom{k}{n}}&\text{if m=0} ,\ \\\frac{\left(-1\right)^{m - 1} \left(k - 2 n\right) {\binom{k}{n}} {\binom{- k + 2 m + 2 n - 1}{m - 1}}}{m} \end{cases} $$

Data table
1	1	-1	2	-5	14	-42
1	-1	2	-5	14	-42	132
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 #333: Right on x
Pyramid #335: Left on x

Export

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