A grocer stacks oranges in a four-sided pyramid that is 7 layers high. How many oranges are in the pile?

Question

anonymous · Answer

Each level is a triangle, nth row from top has n oranges on a side. 
What do the triangles look like? 

x 
1 orange in row 
1 orange in total 

x 
xx 
3 oranges 
4 in total 

x 
xx 
xxx 
6 oranges 
10 in total 

x 
xx 
xxx 
xxxx 
10 oranges 
20 in total 

1 3 6 10... what's the general formula? 
n (n+1) / 2 oranges in nth row 
You should recognize this as the sum of the numbers from 1 to n, which should be obviously correct. 

1 4 10 20...what's the general formula? 
(n^3 + 3n^2 +2n)/6 
I got this using Excel and trial and error. Someone may recognize this as some well-known formula, but I couldn't. It fits the data for n up to 45, which is as many rows as I carried it.
@kchauuu