Pyramid 851

Pyramid #850

Pyramid #851

Pyramid #852

Generating function

$$U_{851}(x, y) = \frac{- 2 x - \sqrt{4 x + 1} - 1}{2 y - 2}$$

Explicit formula

$$T_{851}(n, m, k) = \begin{cases}{\binom{k + m - 1}{m}}&\text{if n = 0} ,\ \\\frac{2 \left(-1\right)^{n - 1} k {\binom{- 2 k + 2 n - 1}{n - 1}} {\binom{k + m - 1}{m}}}{n}&\text{if n > 0} \end{cases} $$

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

Pyramid #850: Right on x

Export

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

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

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