[gumpzilla]

Well, it looks to me like the sentence that describes that sequence is (in white for those who don't want to be spoiled): <font color="white"> {f(1) / f(0)} = 1, and for all other n, {f(n) / f(n-1)} is equal to the greatest power of 2 that divides f(n).</font>

Having looked at the first 20 or so values I'm pretty confident that's right, but I haven't an idea about the proof yet. I'll think about that for a while.