User blog comment:Deedlit11/Ordinal notations II: Up to the Bachmann-Howard ordinal/@comment-1605058-20130629142358/@comment-5529393-20130629182700

Actually, I defined fundamental sequences for all ordinals;  the length of the fundamental sequence is the cofinality of the ordinal. So ordinals of cofinality \(\omega\) will have regular fundamental sequences, ordinals of cofinality \(\Omega\) will get fundamental "sequences" of length \(\Omega\), and successor ordinals will get fundamental sequences of length 1, which will consist of the predecessor ordinal.

So when a is a successor ordinal, a[0] is the predecessor ordinal, and w^a [n] = w^{a[0]) * n is correct.