Understanding Pascal's Pyramid & Internal Entries

[davedave]

I have heard that Pascal's pyramid is a 3-dimensional analogue of Pascal's triangle .

The edges of Pascal's pyramid come from a particular row in Pascal's triangle.

For example, let's take the row of Pascal's triangle having entries 1 5 10 10 5 1.

So, the corresponding Pascal's Pyramid is given below.

1
5 5
10 20 10
10 30 30 10
5 20 30 20 5
1 5 10 10 5 1

Can someone explain how to find the internal entries, such as 20 and 30?

Thanks.

 

[g_edgar]

In general,
$$\frac{(i+j+k)!}{i! j! k!}$$
You did the ones where $i+j+k=5$