7. Express the polynomial in $x$, $f(x)=1-x+x^{2}-x^{3}+\cdots-x^{19}+x^{20}$, as a polynomial in $y$, $g(y)=a_{0}+a_{1} y+\cdots+a_{20} y^{20}$, where $y=x-4$. Then $a_{0}+a_{1}+\cdots+a_{20}=$ $\qquad$ .
$$
\begin{array}{l}
a_{0}+a_{1}(x-4)+a_{2}(x-4)^{2}+\cdots+a_{20}(x-4)^{20}=1-x+x^{2}-\cdots+x^{20}=\frac{1-(-x)^{21}}{1+x}, \\
\text { Let } x=5 \text { and we get } a_{0}+a_{1}+\cdots+a_{20}=\frac{1-(-5)^{21}}{6}=\frac{1}{6}\left(5^{21}+1\right) .
\end{array}
$$