#ifdef ONLINE_JUDGE #include #include #else #include #endif using ll = long long; using lll = __int128_t; #define rep(i, n) for (int i = 0, i##_len = (n); i < i##_len; ++i) #define reps(i, n) for (int i = 1, i##_len = (n); i <= i##_len; ++i) #define rrep(i, n) for (int i = ((int)(n)-1); i >= 0; --i) #define rreps(i, n) for (int i = ((int)(n)); i > 0; --i) #define rep2(i, s, n) for (int i = (s); i < (int)(n); i++) #define repc2(i, s, n) for (int i = (s); i <= (int)(n); i++) #define length(v) ((int)(v).size()) constexpr int inf = 2'000'000'000; constexpr ll linf = 4'000'000'000'000'000'000, M7 = 1'000'000'007, M9 = 998'244'353; #define all(v) begin(v), end(v) #define rall(v) rbegin(v), rend(v) using namespace std; using namespace atcoder; using mint = modint998244353; constexpr ll MOD = M9; using mint = static_modint; struct modInv { int n; vector d; modInv() : n(2), d({0, 1}) {} mint operator()(int i) { while (n <= i) d.emplace_back(-d[MOD % n] * (MOD / n)), ++n; return d[i]; } mint operator[](int i) const { return d[i]; } } invs; struct Factorial { int n; vector d; Factorial() : n(2), d({1, 1}) {} mint operator()(int i) { while (n <= i) d.emplace_back(d.back() * n), ++n; return d[i]; } mint operator[](int i) const { return d[i]; } } factorial; struct FactorialInv { int n; vector d; FactorialInv() : n(2), d({1, 1}) {} mint operator()(int i) { while (n <= i) d.emplace_back(d.back() * invs(n)), ++n; return d[i]; } mint operator[](int i) const { return d[i]; } } factorialInv; mint P(int n, int r) { if (n < r || n < 0 || r < 0) return 0; return factorial(n) * factorialInv(n - r); } mint C(int n, int r) { if (n < r || n < 0 || r < 0) return 0; return factorial(n) * factorialInv(r) * factorialInv(n - r); } mint H(int n, int r) { const int _n = n + r - 1; if (_n < r || _n < 0 || r < 0) return 0; return factorial(_n) * factorialInv(r) * factorialInv(_n - r); } int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); int n; cin >> n; vector> dp = vector>(n + 1, vector(n * 2 + 2)); dp[0][0] = 1; rep(i, n) { int m = i * 2 + 1; rep(j, m) { int l = j, r = m - j - 1; dp[i + 1][j + 1] += dp[i][j]; if (j >= 1) dp[i + 1][j + 2] += dp[i][j] * H(l, 2); if (j <= m - 2) dp[i + 1][j] += dp[i][j] * H(r, 2); if (j != 0 && j != m - 1) dp[i + 1][j + 1] += dp[i][j] * l * r; } } rep(i, 2 * n + 1) cout << dp[n][i].val() << endl; return 0; }