Question: > 
> He is a pedant, a sesquipedalianist, an ambivert.
> 
> 
> 

Is this grammatically correct? I am not sure about the use of "a sesquipedalianist".

Answer: 
"He is a pedant, sesquipedalianist, and an ambivert" can be rewritten more compactly as "He is a pedant, sesquipedalianist, and ambivert". You should group together items in a list that require the same indefinite article, and only use it once at the start.

Whether you use 'a' or 'an' at the beginning of a list to suit the first item, you do not need to insert the other indefinite article if one of the subsequent items would require it if written or spoken alone. He is an observer, optician, driver, and sculptor.

"Accrue: to come to one as a gain, addition, or increment."

American Heritage Dictionary (1992)  

[Repeat indefinite articles](https://forum.wordreference.com/threads/repeat-indefinite-article-use-a-strawberry-an-apple-or-a-cranberry.2528143/)
Yes.

These are the rules for a/an articles:

1. ***A*** before words starting with consonant sounds.  

e.g. A man, a university, a yacht...
2. ***An*** before words starting with vowel sounds.  

e.g. An animal, an error...

So the sentence is grammatically correct.