Buggy python submission (verdict: Time Limit Exceeded):
# -*- coding: utf-8 -*-


import sys


class FactMod():
    '''
    modの値が素数の時のfactと組み合わせを求める
    フェルマーの小定理を用いているため、modが素数以外の時は使えない
    '''

    def __init__(self, n, mod):
        '''
        コンストラクタ
        f:nまでの i!の値を　配列に入れる
        inv: (i!)^-1　の値を配列に入れる
        '''
        self.mod = mod
        self.f = [1]*(n+1)
        for i in range(1, n+1):
            self.f[i] = self.f[i-1]*i % mod

        self.inv = [pow(self.f[-1], mod-2, mod)]
        for i in range(1, n+1)[::-1]:
            self.inv.append(self.inv[-1]*i % mod)
        self.inv.reverse()

    def fact(self, n):
        '''
        n!の値を返す
        '''
        return self.f[n]

    def comb(self, n, r):
        '''
        nCrの値を返す
        '''
        ret = self.f[n] * self.inv[n-r]*self.inv[r]
        ret %= self.mod
        return ret


# python template for atcoder1
sys.setrecursionlimit(10**9)
input = sys.stdin.readline

n = int(input())
N = n+1
A = list(map(int, input().split()))
MOD = 10**9+7
already = set()
for i, l in enumerate(A):
    if l in already:
        dup_ind = i
        dup_num = l
        break
    else:
        already.add(l)
before_first_dup_num = A.index(dup_num)
after_dup_num = N-dup_ind-1

F = FactMod(n+1, MOD)
for k in range(1, n+2):
    all_pattern = F.comb(N, k)
    rem_pattern = 0
    for first_rem in range(k):
        before_first_rem = F.comb(
            before_first_dup_num, first_rem) if before_first_dup_num >= first_rem else 0
        after_dup_rem = F.comb(
            after_dup_num, k-1-first_rem) if after_dup_num >= k-1-first_rem else 0
        rem_pattern += before_first_rem*after_dup_rem
    print((all_pattern-rem_pattern+MOD) % MOD)


Fixed submission:
# -*- coding: utf-8 -*-


import sys


class FactMod():
    '''
    modの値が素数の時のfactと組み合わせを求める
    フェルマーの小定理を用いているため、modが素数以外の時は使えない
    '''

    def __init__(self, n, mod):
        '''
        コンストラクタ
        f:nまでの i!の値を　配列に入れる
        inv: (i!)^-1　の値を配列に入れる
        '''
        self.mod = mod
        self.f = [1]*(n+1)
        for i in range(1, n+1):
            self.f[i] = self.f[i-1]*i % mod

        self.inv = [pow(self.f[-1], mod-2, mod)]
        for i in range(1, n+1)[::-1]:
            self.inv.append(self.inv[-1]*i % mod)
        self.inv.reverse()

    def fact(self, n):
        '''
        n!の値を返す
        '''
        return self.f[n]

    def comb(self, n, r):
        '''
        nCrの値を返す
        '''
        ret = self.f[n] * self.inv[n-r]*self.inv[r]
        ret %= self.mod
        return ret


# python template for atcoder1
sys.setrecursionlimit(10**9)
input = sys.stdin.readline

n = int(input())
N = n+1
A = list(map(int, input().split()))
MOD = 10**9+7
already = set()
for i, l in enumerate(A):
    if l in already:
        dup_ind = i
        dup_num = l
        break
    else:
        already.add(l)
before_first_dup_num = A.index(dup_num)
after_dup_num = N-dup_ind-1

F = FactMod(n+1, MOD)
for k in range(1, n+2):
    all_pattern = F.comb(N, k)
    rem_pattern = F.comb(before_first_dup_num+after_dup_num,
                         k-1) if before_first_dup_num+after_dup_num >= k-1 else 0
    print((all_pattern-rem_pattern+MOD) % MOD)

Buggy python submission (verdict: Time Limit Exceeded):
# -*- coding: utf-8 -*-


import sys


class FactMod():
    '''
    modの値が素数の時のfactと組み合わせを求める
    フェルマーの小定理を用いているため、modが素数以外の時は使えない
    '''

    def __init__(self, n, mod):
        '''
        コンストラクタ
        f:nまでの i!の値を　配列に入れる
        inv: (i!)^-1　の値を配列に入れる
        '''
        self.mod = mod
        self.f = [1]*(n+1)
        for i in range(1, n+1):
            self.f[i] = self.f[i-1]*i % mod

        self.inv = [pow(self.f[-1], mod-2, mod)]
        for i in range(1, n+1)[::-1]:
            self.inv.append(self.inv[-1]*i % mod)
        self.inv.reverse()

    def fact(self, n):
        '''
        n!の値を返す
        '''
        return self.f[n]

    def comb(self, n, r):
        '''
        nCrの値を返す
        '''
        ret = self.f[n] * self.inv[n-r]*self.inv[r]
        ret %= self.mod
        return ret


# python template for atcoder1
sys.setrecursionlimit(10**9)
input = sys.stdin.readline

n = int(input())
N = n+1
A = list(map(int, input().split()))
MOD = 10**9+7
already = set()
for i, l in enumerate(A):
    if l in already:
        dup_ind = i
        dup_num = l
        break
    else:
        already.add(l)
before_first_dup_num = A.index(dup_num)
after_dup_num = N-dup_ind-1

F = FactMod(n+1, MOD)
for k in range(1, n+2):
    all_pattern = F.comb(N, k)
    rem_pattern = 0
    for first_rem in range(k):
        before_first_rem = F.comb(
            before_first_dup_num, first_rem) if before_first_dup_num >= first_rem else 0
        after_dup_rem = F.comb(
            after_dup_num, k-1-first_rem) if after_dup_num >= k-1-first_rem else 0
        rem_pattern += before_first_rem*after_dup_rem
    print((all_pattern-rem_pattern+MOD) % MOD)


Fixed submission:
# -*- coding: utf-8 -*-


import sys


class FactMod():
    '''
    modの値が素数の時のfactと組み合わせを求める
    フェルマーの小定理を用いているため、modが素数以外の時は使えない
    '''

    def __init__(self, n, mod):
        '''
        コンストラクタ
        f:nまでの i!の値を　配列に入れる
        inv: (i!)^-1　の値を配列に入れる
        '''
        self.mod = mod
        self.f = [1]*(n+1)
        for i in range(1, n+1):
            self.f[i] = self.f[i-1]*i % mod

        self.inv = [pow(self.f[-1], mod-2, mod)]
        for i in range(1, n+1)[::-1]:
            self.inv.append(self.inv[-1]*i % mod)
        self.inv.reverse()

    def fact(self, n):
        '''
        n!の値を返す
        '''
        return self.f[n]

    def comb(self, n, r):
        '''
        nCrの値を返す
        '''
        ret = self.f[n] * self.inv[n-r]*self.inv[r]
        ret %= self.mod
        return ret


# python template for atcoder1
sys.setrecursionlimit(10**9)
input = sys.stdin.readline

n = int(input())
N = n+1
A = list(map(int, input().split()))
MOD = 10**9+7
already = set()
for i, l in enumerate(A):
    if l in already:
        dup_ind = i
        dup_num = l
        break
    else:
        already.add(l)
before_first_dup_num = A.index(dup_num)
after_dup_num = N-dup_ind-1

F = FactMod(n+1, MOD)
for k in range(1, n+2):
    all_pattern = F.comb(N, k)
    rem_pattern = F.comb(before_first_dup_num+after_dup_num,
                         k-1) if before_first_dup_num+after_dup_num >= k-1 else 0
    print((all_pattern-rem_pattern+MOD) % MOD)