My personal favorites are the following:

1. Introduction to Combinatorial analysis --- Riordan
2. Concrete Mathematics --- Graham, Knuth, Patashnik
3. Enumerative Combinatorics vol. 1 --- Richard Stanley (is not always that introductory, but for those who like counting, it is a must have)

If you want really easy, but still interesting books, you might like Brualdi's book (though apparently, that book has many mistakes). Also interesting might be some chapters from Feller's book on Probability (volume 1).

My personal favorites are the following:

• Introduction to Combinatorial analysis [Riordan]
• Concrete Mathematics [Graham, Knuth, Patashnik]
• Enumerative Combinatorics vol. $1$ [Richard Stanley]

(is not always that introductory, but for those who like counting, it is a must have)

If you want really easy, but still interesting books, you might like Brualdi's book (though apparently, that book has many mistakes). Also interesting might be some chapters from Feller's book on Probability (volume $1$).