Find the generating function for each of the following sequences. Give the function in closed form, i.e. not in a form involving an infinite sum, but as 1/1 - x or so. 1, 2, 1, 1, 1, 1, 1, 1, ellipsis (b) 1, 0, 0, 2, 0, 0, 3, 0, 0, 4, 0, 0, 5, 0, 0, ellipsis (c) 1, 3, 6, 9, 12, 15, 18, 21, ellipsis (d) 1, 3, 9, 27, 81, 243, 729, ellipsis (e) 1, 1, 1, 2, 2, 2, 4, 4, 4, 8, 8, 8, 16, 16, 16, ellipsis Find the generating function for each of the following sequences. Give the function in closed form, i.e. not in a form involving an infinite sum, but as 1/1 - x or so. 1, 2, 1, 1, 1, 1, 1, 1, ellipsis (b) 1, 0, 0, 2, 0, 0, 3, 0, 0, 4, 0, 0, 5, 0, 0, ellipsis (c) 1, 3, 6, 9, 12, 15, 18, 21, ellipsis (d) 1, 3, 9, 27, 81, 243, 729, ellipsis (e) 1, 1, 1, 2, 2, 2, 4, 4, 4, 8, 8, 8, 16, 16, 16, ellipsis