Finding a formula for a sequence

brumby_3

Find a simple formula which defines the nth term of a sequences whose first few terms are the same as those given:

1, -4, 9, -16

$$\displaystyle 1, -4, 9, -16, \dots =1^2, -2^2, 3^2, -4^2, \dots =-(-1)^1\times 1^2, -(-1)^2\times 2^2, -(-1)^3\times$$ $$\displaystyle 3^2, -(-1)^4\times 4^2, \dots$$