write a go solution for Description:
Consider every tree (connected undirected acyclic graph) with n vertices (n is odd, vertices numbered from 1 to n), and for each 2<=i<=n the i-th vertex is adjacent to exactly one vertex with a smaller index.

For each i (1<=i<=n) calculate the number of trees for which the i-th vertex will be the centroid. The answer can be huge, output it modulo 998,244,353.

A vertex is called a centroid if its removal splits the tree into subtrees with at most (n-1)/2 vertices each.

Input Format:
The first line contains an odd integer n (3<=n<2*10^5, n is odd) — the number of the vertices in the tree.

Output Format:
Print n integers in a single line, the i-th integer is the answer for the i-th vertex (modulo 998,244,353).

Note:
Example 1: there are two possible trees: with edges (1-2), and (1-3) — here the centroid is 1; and with edges (1-2), and (2-3) — here the centroid is 2. So the answer is 1,1,0.

Example 2: there are 24 possible trees, for example with edges (1-2), (2-3), (3-4), and (4-5). Here the centroid is 3.. Output only the code with no comments, explanation, or additional text.