What is the compile-time type of the "throw" expression in C# 7?

In C# 7 it is possible to raise an exception inside an expression:

int n = list != null ? list.Count : throw new NullReferenceException("list");

In this position, the throw expression can substitute an expression of any type.

Now I want to define a function that executes some action before raising an exception:

??? DoSomethingAndThrowException(Exception e)
{
    MessageBox.Show("Prepare for an exception!");
    throw e;
}

What would be the return type of such function, so that it can be used in the same places as the original throw expression:

int n = list != null ? list.Count : DoSomethingAndThrowException(new NullReferenceException("list"));

There's the option to declare it as a generic method:

T DoSomethingAndThrowException<T>(Exception e) {...}

But this seems cumbersome, as the generic type doesn't occur anywhere in the function body. Is this the only way to do it, or is there some type I don't know of, and which is assignable to any type (an "anti-object" type, so to speak)?