What is the difference between a class having private constructor and a sealed class having private constructor?

Yes A can be inherited by a nested class, while B cannot be inherited at all. This is perfectly legal.

Based on the second article if this is the only constructor you will not be able to create an instance of Class A or Class B. Because Class A has a private constructor you cannot derive from it due to its protection level, nor can you derive from B with sealed.

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