Counting in Two Ways

We can count stuff in various ways:

1. A recurrence relation e.g. and
2. A closed formula e.g.
3. A generating function e.g.
4. Asymptotic formula
5. An algorithm
   Binomial Coefficient
   Falling Factorial
   Rising Factorial
   Multinomial Coefficient
   Stirling Number of the Second Kind
   Sum of Powers
   Stirling Number of the First Kind
   Burnside’s Lemma
   Fibonacci Sequence