Time complexity of Heap's Algorithm

Question

I'm studying time complexity of recursive algorithms and I want to know the complexity of the Heap's algorithm that generate all possible permutations of n objects.

procedure generate(k : integer, A : array of any):
    if k = 1 then
        output(A)
    else
        // Generate permutations with kth unaltered
        // Initially k == length(A)
        generate(k - 1, A)

        // Generate permutations for kth swapped with each k-1 initial
        for i := 0; i < k-1; i += 1 do
            // Swap choice dependent on parity of k (even or odd)
            if k is even then
                swap(A[i], A[k-1]) // zero-indexed, the kth is at k-1
            else
                swap(A[0], A[k-1])
            end if
            generate(k - 1, A)

        end for
    end if

I think the time complexity of this is O(n * n!) but I'm not sure. All the help would be appreciated. Thank you.