summation notation of -1+2+7+14+23...

If n is an integer then your series is given by ∑_{k=1 to n(}k² - 2)

k      k² - 2    ∑_{k=1 to n(}k² - 2)

1        -1           -1

2          2            1

3          7            8

4          14          22

5          23          45

...

summation notation of -1+2+7+14+23...

What I noticed is that if I add 2 to each of these terms I get

1+4+9+16+     familiar?

sum of  n^2-2

 

$$\displaystyle\sum_{n=1}^\infty\;(n^2-2)$$