Create n-dimensional vector with given sizes

So, what I want is to create multidimensional vector of given type where the first dimension will have size of the first argument of a function call, etc, for example if I do

std::size_t n = 5;
auto x = make_vector<int>(n + 1, n * 2, n * 3);

x should be 6x10x15 3d array (consisting of zeroes, because I want to default construct right now)

I have tried this:

template <typename T>
std::vector<T> make_vector(std::size_t size) {
    return std::vector<T>(size);
}

template <typename T, typename... Args>
auto make_vector(std::size_t first, Args... sizes) -> std::vector<decltype(make_vector<T>(sizes...))> {
    auto inner = make_vector<T>(sizes...);
    return std::vector<decltype(inner)>(first, inner);
}

It seems to work for 1 or 2 arguments, but fails for 3 arguments with following error(clang++)

In file included from /Users/riad/ClionProjects/for-jhelper/output/run.cpp:1:
/Users/riad/ClionProjects/for-jhelper/tasks/TaskC.cpp:12:12: error: no matching function for call to 'make_vector'
                auto x = make_vector<int>(n + 1, n * 2, n * 3);
                         ^~~~~~~~~~~~~~~~
/Users/riad/ClionProjects/for-jhelper/tasks/../spcppl/make_vector.hpp:9:6: note: candidate template ignored: substitution failure [with T = int, Args = <unsigned long, unsigned long>]: call to function 'make_vector' that is neither visible in the template definition nor found by argument-dependent lookup
auto make_vector(std::size_t first, Args... sizes) -> std::vector<decltype(make_vector<T>(sizes...))> {
     ^                                                                     ~~~~~~~~~~~
/Users/riad/ClionProjects/for-jhelper/tasks/../spcppl/make_vector.hpp:4:16: note: candidate function template not viable: requires single argument 'size', but 3 arguments were provided
std::vector<T> make_vector(std::size_t size) {

If I understand correctly problem is that when compiler tries to calculate return value of make_vector it have to know the return value of vector with less number of arguments and fails to do so. How do I fix that?