Chomsky Classification of Languages
The language $A = \{ a^n\:b\:c^{2n}\:b^m |\; n ∈ N^{+} ;\; m ∈ N \}$ is not obviously regular since finite automata do not have memory and hence it is not possible for them to determine the relation between $a$ and $c$.

Let us try to construct a Type-2 grammar for this language. Note that Type-2 grammars are of the form  $V\to(V \cup T)^{*}$ where $V$ represents non-terminals and $T$ represents terminals. So our example would lead to something like this:

$S \to a\:A_1\:cc\:A_2 $

$A_1 \to a\:A_1\:cc\;|\;b$

$A_2 \to b\:A_2\;|\;\epsilon$

Hence we see that this is a Type-2 grammar according to the Chomsky hierarchy.