how did confucius influence the han dynasty

As far as I know, from Emperor Wdui, the Confucianism became the rules for the whole society. The system of the government is based on it to establish.
People who want to become an official needed to study the Confucianism and the philosophy controlled Chinese culture from then on.

He did not have a huge impact on the Han dynasty. The dynasty he most influenced was the Ming dynasty I think.