New math problem
Let C(n) be the number of ways to write n as the sum of consecutive non-negative integers. The terms from C(0) to C(10) are 1, 2, 1, 3, 1, 2, 3, 2, 1, 3, 3. Find an ordinary generating function for C(n) in closed form, in terms of elementary functions if possible. Prove that the series 1/C(n) diverges. When about the series 1/(n C(n)). What is the tightest order-of-magnitude estimate of C(n) that you can find? Prove that C(n) is unbounded. How frequently does it occur that C(n) is equal to a given number k? Tell me something I don't know about C(n).