Divide them by the number of term 1,2,3,4 and see what we get:

-1,2,7,14

Add 2 to those

1,4,9,16

Aha!~  The squares!  Now let's start with the squares and go backward

We ended up with the squares,

So we start with the squares, 

1,4,9,16

Before that we added 2,

So we will subtract 2,  

-1,2,7,14

Before that we divided by the number of term, n

So we multiply by the number of term n,  

-1,4,21,56



Plug in n=1,2,3,4,5,...

-1, 4, 21, 56, 115, 204, 329, 496, 711, 980, 1309, 1704, 2171, 2716, 
3345, 4064, 4879, 5796, 6821, 7960, ... 

Edwin