4. The polynomial $\left(x^{2}+2 x+2\right)^{2001}+\left(x^{2}-3 x-\right.$ $3)^{2001}$ is expanded and like terms are combined. The sum of the coefficients of the odd powers of $x$ in the resulting expression is $\qquad$.
4. -1 .
$$
\text { Let } \begin{aligned}
f(x)= & \left(x^{2}+2 x+2\right)^{2001}+\left(x^{2}-3 x-3\right)^{2001} \\
= & A_{0}+A_{1} x+A_{2} x^{2}+\cdots+A_{4001} x^{4001} \\
& +A_{4002} x^{4002} .
\end{aligned}
$$
$$
\begin{array}{l}
\text { Then } A_{0}+A_{1}+A_{2}+\cdots+A_{4001}+A_{4002} \\
\quad=f(1)=0, \\
A_{0}-A_{1}+A_{2}-\cdots-A_{4001}+A_{4002} \\
=f(-1)=2 .
\end{array}
$$

Subtracting the two equations gives $2\left(A_{1}+A_{3}+\cdots+A_{4001}\right)=-2$.
$$
\text { Therefore, } A_{1}+A_{3}+\cdots+A_{4001}=-1 \text {. }
$$