Much simpler solution for generating a string of balanced parentheses of length (n * 2).

GenerateParentheses.swift

import Foundation

final class Generator {

    private var store = [[""]]

    func genBalanced(_ n: Int) -> [String] {
        if n < store.count {
            return store[n]
        }

        var result: [String] = []
        for i in 0..<n {
            for x in genBalanced(i) {
                for y in genBalanced(n - i - 1) {
                    result.append("(" + x + ")" + y)
                }
            }
        }

        store.append(result)
        return store[n]
    }
}