I need to solve the exact time complexity for the brute force version of the Traveling Salesman using a recurrence relation.
I've worked out the recurrence relation to be as follows: T(n)=T(n-1)*(n-1)+1
But I'm having trouble reducing that that to a closed form of the function, and thus get the exact time complexity. Not for lack of trying either. It's looking like it's coming out as a binomial sequence but my algebra is a bit rusty.
If anyone could help or point me on the right path I would appreciate it.