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

Show that the generating function [itex]A(x) = \sum_n a_n x^n[/itex] of

[tex]a_n = \sum_{k=0}^n {n+k \choose 2k} 2^{n-k}[/tex]

satisfies

[tex]A(x) = \frac{1-2x}{4x^2-5x+1}[/tex]

2. Relevant equations

3. The attempt at a solution

A hint was given to "interchange the sums". After doing that, I don't see how to proceed. I also obtained the coefficients by partial fractions on A(x) but it's definitely non-trivial to show these are a_n. Thanks for any help.

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

Dismiss Notice

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: Generating functions and sums with binomial coefficients

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