#include <bits/stdc++.h>
using namespace std;
constexpr int N = 5000 + 5;
constexpr int mod = 998244353;
typedef long long ll;
inline ll quickpow(ll a, int b)
{
	ll res = 1;
	while (b)
	{
		if (b & 1)
			(res *= a) %= mod;
		(a *= a) %= mod;
		b >>= 1;
	}
	return res;
}
int n;
ll fac[N], ifac[N];
inline ll C(int _n, int _m)
{
	if (_m < 0 || _n < _m)
		return 0;
	return fac[_n] * ifac[_m] % mod * ifac[_n - _m] % mod;
}
vector<int> G[N];
int sze[N];
ll f[N];
inline void dfs1(int u)
{
	f[u] = 1;
	for (int v : G[u])
	{
		dfs1(v);
		sze[u] += sze[v];
		(f[u] *= f[v] * C(sze[u], sze[v]) % mod) %= mod;
	}
	++sze[u];
}
ll g[N][N];
inline void dfs2(int u)
{
	for (int v : G[u])
	{
		ll sum = 0;
		ll times = f[u] * quickpow(f[v] * C(sze[u] - 1, sze[v]) % mod, mod - 2);
		for (int i = 1; i <= n; ++i)
		{
			(sum += g[u][i - 1] * C(n - i + 1 - sze[v], sze[u] - sze[v] - 1)) %= mod;
			(g[v][i] += sum * times) %= mod;
		}
		dfs2(v);
	}
}
inline void _main()
{
	cin >> n;
	for (int i = 2; i <= n; ++i)
	{
		int _fa;
		cin >> _fa;
		G[_fa].push_back(i);
	}
	fac[0] = 1;
	for (int i = 1; i <= n; ++i)
		fac[i] = fac[i - 1] * i % mod;
	ifac[n] = quickpow(fac[n], mod - 2);
	for (int i = n; i >= 1; --i)
		ifac[i - 1] = ifac[i] * i % mod;
	dfs1(1);
	g[1][1] = 1;
	dfs2(1);
	for (int i = 1; i <= n; ++i)
		cout << g[i][i] * f[i] % mod * C(n - i, sze[i] - 1) % mod << ' ';
	cout << '\n';
}
signed main()
{
	ios::sync_with_stdio(false);
	cin.tie(0), cout.tie(0);
	int test = 1;
	while (test--)
		_main();
	return 0;
}