I have the product

sin(x)/x

= (1 - x^2/pi^2)(1 - x^2/4pi^2)(1 - x^2/9pi^2)(1 - x^2/16pi^2)......

But i'm looking to expand the whole product and find only the term in x^k, for some general k. and find an expression for this general coefficient.

I know I can equate it to the Taylor series, but I want to do it this way to get a different expression. Please help, thanks!