Summation for a Python function

[BK124]

Homework Statement

For formatting sake I've copied a picture of the problem and attached it here: http://i.imgur.com/kOjTy.png

Im not worried about the coding part right now I feel I can handle that, my main issue is trying to understand how the values in the summation are derived. It seems simple enough, but I can't seem to grasp how they got the 10 values in the example there. Once I understand the summation, the coding should be easy. I just need a bit of guidance in how it all's working.

Homework Equations

Cn+1 = Ʃ Ck Cn-k from k = 0 to n

The Attempt at a Solution

Obviously
C0 = 1

Beyond that, here's what my understanding of it seems to be:
For C1
k starts at 0
C1 = C0 * C1-0 + C1 * C1-1

but this is where I get confused.

 

[jambaugh]

I suspect one defines the process recursively. How many ways can you draw a line segment between vertices? Each way divides the polygon into two smaller polygons.

You may then have to be careful iterating cases in a way that avoids double counting.

 

[earlofwessex]

Cn+1 = Ʃ Ck Cn-k from k = 0 to n

The Attempt at a Solution

Obviously
C0 = 1

Beyond that, here's what my understanding of it seems to be:
For C1
k starts at 0
C1 = C0 * C1-0 + C1 * C1-1

but this is where I get confused.

hmm, i think you are reading the summation notation wrong, C_n+1 doesn't come into the equation, only C_n, the previous term.
C₁ = C₀*C₀ = 1
C₂ = C₀*C₁ + C₁*C₀ = 2
C₃ = C₀*C₂ + C₁*C₁ + C₂*C₀ = 5
C₄ = C₀*C₃ + C₁*C₂ + C₂*C₁ + C₃*C₀ = 14
and so on...