Unraveling 1999 Putnam A3: Understanding the Recurrence Relation

[ehrenfest]

Homework Statement

In the first solution to 1999 A3 at the this website:
http://www.unl.edu/amc/a-activities/a7-problems/putnam/-pdf/1999s.pdf

You do not need to read the problem.

I do not see hot they go the recurrence relation in the first sentence. Specifically I do not follow reason why their first expression "yields the recurrence..."?

Homework Equations

The Attempt at a Solution

 

[Hurkyl]

Did you try multiplying it out and collecting like terms?

 

[ehrenfest]

Yes. But you still have that one on the other side. I do not know what to do with that.

 

[Hurkyl]

I'm not sure what you mean. You have an equation; the two sides are equal.

 

[ehrenfest]

I am saying the 1 is outside of the summation. I need to have everything in a summation before I can get the desired result, don't I?

 

[Hurkyl]

Both sides of the equation are power series. What has to be true for two power series to be equal?

 

[ehrenfest]

I see. The coefficients of all powers of x greater than 0 must b 0 and the coefficient of x^0 must be 1.