The question has arisen for those of you who have not found the formula for Er(n) whether to go ahead and write up your IA with the work you've done. I asked for guidance from some of my IB gurus and they said "don't have them write it up without the formula". They also said this:
If I give you hints but you write it up, it can still be considered your work.
If I straight up give you the answer, then presumably it cannot.
So here are my strongest hints which I hope you will find enlightening. Lacsap is Pascal spelled backwards. There is a famous triangle that Blaise Pascal explored that has lots of interesting patterns. I think you will find the numerator pattern if you explore Pascal's triangle. Try this website:http://www.mathsisfun.com/pascals-triangle.html For the denominator take a look at the pattern that is created by r(n - r). Coupled with your results for the numerator, you may find what you're after.
Please email me if that doesn't help,
Mr. Alei