Find coefficient of x in a generating function The problem is as follows:
$\text{Determine the coef. of } x^{10} \text{ in } (x^3 + x^5 + x^6)(x^4 + x^5 + x^7)(1+x^5+x^{10}+x^{15}+...)$

I factored out some $x$'s, to get $x^3(1+x^2+x^3)x^4(1+x+x^3)(1+x^5+x^{10}+x^{15}+...)$and then combined the factored terms to get  $x^7(1+x^2+x^4)(1+x+x^3)(1+x^5+x^{10}+x^{15}+...)$

Now I don't know what to do; usually it ends up factoring to $(1+x+x^2+...)$, but that doesn't appear to be the case here.

Hint :
coefficient of $x^3$ in $(1+x^2+x^3)(1+x+x^4)(1+x^5+x^{10}+x^{15}+...)$ is $2$, because
$x^3=x^3\times 1 \times 1, x^3= x^2\times x \times 1$
