How to inherit constructors?

Yes, you have to copy all 387 constructors. You can do some reuse by redirecting them:

  public Bar(int i): base(i) {}
  public Bar(int i, int j) : base(i, j) {}

but that's the best you can do.

Yes, you will have to implement the constructors that make sense for each derivation and then use the base keyword to direct that constructor to the appropriate base class or the this keyword to direct a constructor to another constructor in the same class.

If the compiler made assumptions about inheriting constructors, we wouldn't be able to properly determine how our objects were instantiated. In the most part, you should consider why you have so many constructors and consider reducing them to only one or two in the base class. The derived classes can then mask out some of them using constant values like null and only expose the necessary ones through their constructors.

Update

In C#4 you could specify default parameter values and use named parameters to make a single constructor support multiple argument configurations rather than having one constructor per configuration.

387 constructors?? That's your main problem. How about this instead?

public Foo(params int[] list) {...}