If \(p(n)\) denotes the number of integer partitions of \(n\in\mathbb{N}\), prove that
\[p(n) < \dfrac{3n}{n+2} C_n\]
where \(C_n\) is the \(n\)th Catalan number for all natural \(n\).
Catalan Inequality
- What is the value of the contour integral around Western Europe?
- Zero.
- Why?
- Because all the poles are in Eastern Europe.
Revive the IMO marathon.
- Zero.
- Why?
- Because all the poles are in Eastern Europe.
Revive the IMO marathon.
Re: Catalan Inequality
Hint
- What is the value of the contour integral around Western Europe?
- Zero.
- Why?
- Because all the poles are in Eastern Europe.
Revive the IMO marathon.
- Zero.
- Why?
- Because all the poles are in Eastern Europe.
Revive the IMO marathon.