(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I need to prove two things about the Catalan numbers. The first is that Cn is odd iff n=(2^k)-1 for some positive integer k.

The second is that given the matrix A defined by the rule a(i,j)=C(i+j), prove that det A=1. I have not covered determinants in my linear class yet, so I do not have any idea what to do with this one.

2. Relevant equations

3. The attempt at a solution

I am assuming that both proceed by induction. The first one seems to be more direct, but I am really lost as to how to proceed with both. Any help or suggestions is greatly appreciated. Thanks a lot!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Proofs involving Catalan Numbers

**Physics Forums | Science Articles, Homework Help, Discussion**