P6597 Alkene Counting

You may need: + [Alkyl Counting](https://loj.ac/problem/6538) + [Alkane Counting](https://loj.ac/problem/6512) Since Luogu does not have the two problems above, this problem is made instead.

Find the number of isomers of **alkenes (homologs of ethylene)** with chemical formula $\text{C}_n \text{H}_{2n}$. In this problem, stereoisomerism and cis-trans isomerism are not considered. The answer should be taken modulo $998244353$.

A positive integer $n$.

Output a total of $n-1$ lines, where the $i$-th line is the answer for alkenes with $2 \sim n$ carbon atoms.

#### Explanation for Sample 1 + $n=2$: ethylene. + $n=3$: propylene. + $n=4$: 1-butene; 2-butene; 2-methyl-1-propene. + $n=5$: 1-pentene; 2-pentene; 2-methyl-1-butene; 3-methyl-1-butene; 2-methyl-2-butene. #### Constraints For $100\%$ of the testdata, it is guaranteed that $1 \leq n \leq 100000$. Translated by ChatGPT 5