Equivalent to?
I am Danish.
I am a Danish.
“Berliner” could be a noun, a resident of Berlin (or a kind of pastry, sometimes translated “donut”) or it could be the nominiative singular masculine form of the adjective describing a person from Berlin. That’s why I deliberately chose “American” in my analogy, it could be a noun or adjective and works both ways, with the noun taking the indefinite artcle “an” just as in German it would take the article “ein”. With Dane/Danish the noun and adjectives have distinct forms.
Like I said, I’ve heard both takes on it from Germans. In the event the crowd absolutely loved it, especially in his nasal Boston accent. Or is that Bostonian accent? Or Bostoner?