Generating functions (Expansion) Problem: Give an interpretation in partition terms for the coefficient $x^{12}$ in the expansion $(1+x^2+x^4+x^6+x^8+x^{10}+x^{12})(1+x^4+x^8+x^{12})(1+x^6+x^{12})(1+x^8)(1+x^{10})(1+x^{12})$
I'm not sure if I have to find a generating function or only determine when $x^{12}$ appears or only try to describe his behavior.
Thanks for your help.

That's the same as the coefficient of $x^6$ in
$$(1+x+x^2+x^3+x^4+x^5+x^6)(1+x^2+x^4+x^6)(1+x^3+x^6)(1+x^4)(1+x^5)(1+x^6)$$
which is the same as the coefficient of $x^6$ in
$$(1+x+x^2+\cdots)(1+x^2+x^4+
\cdots)(1+x^3+x^6+\cdots)\cdots=
\prod_{n=1}^\infty\frac1{1-x^n}$$
which must be the number of partitions of some or other number....
