38. a. The sequence of Catalan numbers is defined recursively by an)- C(k-1)C(n-k) for n 2 Compute the values of C(2), C(3), and C(4) using this recurrence relation. b. Frank and Jody are both candidates for president of the County Council. The number of votes cast equals 2n, where n votes are cast for Frank and for Jody. Votes are counted sequentially. The ballot problem asks: In how many ways can the votes be counted so that Jody's total is never ahead of Frank's total? The answer, as it turns out, is an), the nth Catalan number. For example, if, 5, one possible counting sequence that meets this requirement is FFJJFJFFJJ Using n = 3, write down all the satisfactory counting sequences and compare the result to the Catalan number C(3)