Time complexity of Tsp using DP
Your algorithm is known as the Held–Karp algorithm, and is described on Wikipedia, and also mentioned on the Wikipedia page on the traveling salesman problem.
Your implementation of the algorithm is wasteful. Using memoization, there are only at most $n2^n$ inputs. Since TSP runs in time $O(n)$ ignoring recursive calls, when using memoization, the total running time will be $O(n^22^n)$.