Given that $n$ is a natural number, the polynomial
$$
P(x)=\sum_{h=0}^{n} c_{n}^{h} x^{n-h}(x-1)^{h}
$$

can be expanded into an ascending power series of $x$: $a_{0}+a_{1} x+a_{2} x^{2}+\cdots+a_{n} x^{n}$. Find
$$
\left|a_{0}\right|+\left|a_{1}\right|+\left|a_{2}\right|+\cdots+\left|a_{n}\right|
$$
$$
P(x)=(x+x-1)^{n}=(2 x-1)^{n}=\sum_{k=0}^{n} C_{n}^{k}(2 x)^{k}(-1)^{n k}
$$

So
$$
\sum\left|a_{k}\right|=\sum_{k=0}^{n} C_{n}^{k} 2^{k}=3^{n}
$$