Isn't it amazing how fast one can make incorrect code? ;-)

Here is a fixed version of my partial_product3, but now it is no faster than partial_product.

def partial_product3(j, i):
    a = [l << 1 | 1 for l in range(j, i + 1)]
    n = len(a)
    while 1:
        if n == 1:
            return a[0]
        half = n//2
        for k in range(0,half):
            a[k] = a[k*2] * a[k*2+1]
        if n & 1:
            a[half] = a[n-1]
            n = half + 1
        else:
            n = half