Questions & Answers about Herzlichen Glückwunsch!
Because herzlichen is the inflected form of the adjective herzlich.
In Herzlichen Glückwunsch!, Glückwunsch is a masculine noun, and this fixed expression uses the accusative singular form. For a masculine noun in the accusative, the adjective takes -en:
- herzlicher Glückwunsch = nominative
- herzlichen Glückwunsch = accusative
So herzlichen is the grammatically correct form in this expression.
Because this is a fixed exclamation or set phrase. German often uses short expressions without a verb, especially in greetings, wishes, and polite formulas.
Compare:
- Guten Morgen!
- Gute Besserung!
- Herzlichen Glückwunsch!
English does the same thing with Congratulations! There is no verb there either, but it still works as a complete expression.
In these short formulaic expressions, German often leaves out the article.
So instead of something fuller, German simply says:
- Herzlichen Glückwunsch!
This is completely normal and idiomatic. You do not need to add einen when using it as a standalone congratulation.