申論題

6. Consider the number of the partitions of a positive integer into positive summands without regard to order. For example, 4 = 1+1+1+1 = 1+1+2 = 2+2 = 1+3, so the integer 4 has five partitions. Find the generating function for the number of the partitions of a positive integer n into positive summands where each summand appears at most twice in each of the partitions. Please express your generating function in a closed form and indicate how to find the number of the partitions of n from your generating function.