Find the number of 5-combinations of the multi-set {4*a, 4*b, 4*c} using generating functions.
Because I am finding combinations I know that I have to use ordinary generating functions and not exponential generating functions.
I can first represent this as $$(1+x+x^2+x^3+x^4)(1+x+x^2+x^3+x^4)(1+x+x^2+x^3+x^4)$$ $$=(1+x+x^2+x^3+x^4)^3$$
I'm not sure where to go from here though- I would greatly appreciate any advice or help! Thanks.
This is the coefficient of $x^5$ in the expansion of $(1+x+x^2+x^3+x^4)^3 = (1-x^5)^3/(1-x)^3 = (1-3x^5 +3x^{10} -x^{15})\displaystyle\frac{1}{(1-x)^3} $. Can you find a taylor series expansion for the second term in the product?