They are called Melodeons. There are two basic types. Irish style where the two rows are a half step apart such as B/C or C#/D. The other is German/Vienneese where the two rows are a fifth apart C/G or G/D. The Norteno accordion is a Vienneese with the left hand buttons removed, and the cajun accordion is a single row diatonic that comes in various keys.

I play a German C/G and my left hand chord/bass buttons are C,G,F,E, Amin,D.