Surprise!

Consider the sequence \(x(n)\) where \(x(0)=1\) and \(x(n) = (1+ x(0)^2 + x(1)^2+...+x(n-1)^2) / n\). The sequence begins \(1, 2, 3, 5, 10\). Find the smallest \(n\) such that \(x(n)\) is not an integer.

Source: Problem 1385 of the Week from Stan Wagon