MathDB
Counting words!

Source: Romania TST 2014 Day 5 Problem 2

January 21, 2015
functioncombinatorics unsolvedcombinatorics

Problem Statement

Let mm be a positive integer and let AA, respectively BB, be two alphabets with mm, respectively 2m2m letters. Let also nn be an even integer which is at least 2m2m. Let ana_n be the number of words of length nn, formed with letters from AA, in which appear all the letters from AA, each an even number of times. Let bnb_n be the number of words of length nn, formed with letters from BB, in which appear all the letters from BB, each an odd number of times. Compute bnan\frac{b_n}{a_n}.