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