calculating binomial coefficient by simulation of pascals triangle

This is a little problem i set myself, to create a program that dynamically generates Pascals triangle to resolve the binary co-efficient of an index. Unfortunantly ive fallen pretty early on. I cant figure a way to to add the values without creating massive arrays containg hundreds of variables or hard coding the data.

Anybody at all have a suggestion about how i could do it.

i get the value index form the user
the line id of the triangle will be the same as index
the number of variables in the line will be index +1
and this is where i got stuck...

You can use a formula to calculate the k-th number on the n-th line.

(n k) = n! / (k! * (n - k)!)