This is the 4170th most frequent Chinese word.
唯一一
The term "唯一一" is not a standard or meaningful phrase in Chinese. It may be a typo or misinterpretation.
The term '唯一一次' (the only time) specifies the singular occurrence of an event, here emphasizing the rarity of his achievement.
这一奖项是他唯一一次获奖的经历。
This award is his only experience of winning.
Here, '唯一一个' (the only one) highlights exclusivity, denoting the unique person fitting the described role.
她是我唯一一个倾诉自己秘密的朋友。
She is the only friend I confide my secrets in.
In this case, '唯一一棵' (the only one tree) draws attention to the distinctive characteristic of the tree among others in the forest.