Find a closed form equation of the following sequence: ${0,0,-2,0,4,0,-6,...}$ Find a closed form equation of the following sequence: ${{0,0,-2,0,4,0,-6,...}}$
I know $1+-1^n$ = 0 if n is odd and 1 if n is even. 
However finding alternating signs when plugging in only even numbers seems to be difficult. I.e. finding a g(n) such that g(2)=-2, g(4)=4, g(6)=-6, and so forth.

Henning Makholm's comment links to solutions not involving trigonometry.  Here is a simple real expression which does:
$$n \cos\left(\frac{n\pi}{2}\right).$$  
