A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2015; you can also visit the original URL.
The file type is `application/pdf`

.

##
###
A Short Approach to Catalan Numbers Modulo $2^r$

2011
*
Electronic Journal of Combinatorics
*

We notice that two combinatorial interpretations of the well-known Catalan numbers $C_n=(2n)!/n!(n+1)!$ naturally give rise to a recursion for $C_n$. This recursion is ideal for the study of the congruences of $C_n$ modulo $2^r$, which attracted a lot of interest recently. We present short proofs of some known results, and improve Liu and Yeh's recent classification of $C_n$ modulo $2^r$. The equivalence $C_{n}\equiv_{2^r} C_{\bar n}$ is further reduced to $C_{n}\equiv_{2^r} C_{\tilde{n}}$ for

doi:10.37236/664
fatcat:jb7b3jqbajhfpgvmojmvcxh2iq