Buggy python submission (verdict: Time Limit Exceeded):
import math
import sys
K, N = [int(i) for i in input().split(' ')]
mod = 998244353
sys.setrecursionlimit(100000)

def mul(a, b):
    return ((a % mod) * (b % mod)) % mod

def power(x, y):
    if   y == 0     : return 1
    elif y == 1     : return x % mod
    elif y % 2 == 0 : return power(x, y//2)**2 % mod
    else            : return power(x, (y-1)//2)**2 * x % mod

def div(a, b):
    return mul(a, power(b, mod-2))

def C(n, r):
    if r < 0:
        return 0
    return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))

olist = [C(N+K-2, N) % mod if K!=1 else 0]

def EE(i):
    k2 = int((K - abs(K - int((i-1)/2) * 2) )/2)
    k1 = K - k2*2 - (1 if i % 2 == 0 else 0)
    result = 0
    for j in range(min(k2, N+1)):
        if i % 2 == 1:
            olist[j] = div(olist[j] * k2, k2-j)
        olist[j] = div(olist[j] * (k1+j) , N+k1)
        result = (result + olist[j]) % mod
        if i % 2 == 0 and j != N:
            result = (result + div(olist[j] * (N-j), N+k1-1)) % mod

    if N >= k2:
        if i % 2 == 1:
            olist.append((C(k2, k2) * C(N+k1-1, N-k2) * pow(2, k2)) % mod)
        else:
            if i != 2:
                olist[k2] = div(olist[k2] * (k1+k2), N+k1)
            result = (result + div(olist[k2] * (N-k2), N+k1-1)) % mod
        result = (result + olist[k2]) % mod
    return result

if K == 1:
    print(0)
else:
    result = []
    for i in range(K):
        result.append(str(EE(i+2)))
    print("\n".join(result + result[:-1][::-1]))


Fixed submission:
import math
import sys
K, N = [int(i) for i in input().split(' ')]
mod = 998244353
sys.setrecursionlimit(100000)

def mul(a, b):
    return ((a % mod) * (b % mod)) % mod

def cmb_f(n, r, mod):
#    print(n, r)
    if ( r<0 or r>n ):
        return 0
    r = min(r, n-r)
#    print(g1[n] * g2[r] * g2[n-r] % mod)
    return g1[n] * g2[r] * g2[n-r] % mod

NNN = 10**4
g1 = [1, 1]
g2 = [1, 1]
inverse = [0, 1]

for i in range( 2, NNN + 1 ):
    g1.append( ( g1[-1] * i ) % mod )
    inverse.append( ( -inverse[mod % i] * (mod//i) ) % mod )
    g2.append( (g2[-1] * inverse[-1]) % mod )

def EN(i):
    k2 = int((K - abs(K - int((i-1)/2) * 2) )/2)
    k1 = K - k2*2 - (1 if i % 2 == 0 else 0)
    result = 0
    for j in range(k2+1):
        if N < j:
            break
        result = (result + mul(mul(cmb_f(k2, j, mod) , cmb_f(N+k1-1, j+k1-1, mod)) , pow(2, j) % mod))% mod
    if i % 2 == 1:
        return result
    for j in range(k2+1):
        if N-1 < j:
            break
        result = (result + mul(mul(cmb_f(k2, j, mod), cmb_f(N+k1-2, j+k1-1, mod)), pow(2, j) % mod))% mod
    return result

if K == 1:
    print(0)
else:
    result = []
    for i in range(K):
        result.append(str(EN(i+2)))
    print("\n".join(result + result[:-1][::-1]))

Buggy python submission (verdict: Runtime Error):
import math
import sys
K, N = [int(i) for i in input().split(' ')]
mod = 998244353
sys.setrecursionlimit(100000)

def mul(a, b):
    return ((a % mod) * (b % mod)) % mod

def power(x, y):
    if   y == 0     : return 1
    elif y == 1     : return x % mod
    elif y % 2 == 0 : return power(x, y//2)**2 % mod
    else            : return power(x, (y-1)//2)**2 * x % mod

def div(a, b):
    return mul(a, power(b, mod-2))

def C(n, r):
    if r < 0:
        return 0
    return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))

olist = [C(N+K-2, N) % mod]

def EE(i):
    k2 = int((K - abs(K - int((i-1)/2) * 2) )/2)
    k1 = K - k2*2 - (1 if i % 2 == 0 else 0)
    result = 0
    for j in range(min(k2, N+1)):
        if i % 2 == 1:
            olist[j] = div(olist[j] * k2, k2-j)
        olist[j] = div(olist[j] * (k1+j) , N+k1)
        result = (result + olist[j]) % mod
        if i % 2 == 0 and j != N:
            result = (result + div(olist[j] * (N-j), N+k1-1)) % mod

    if N >= k2:
        if i % 2 == 1:
            olist.append((C(k2, k2) * C(N+k1-1, N-k2) * pow(2, k2)) % mod)
        else:
            if i != 2:
                olist[k2] = div(olist[k2] * (k1+k2), N+k1)
            result = (result + div(olist[k2] * (N-k2), N+k1-1)) % mod
        result = (result + olist[k2]) % mod
    return result

result = []
for i in range(K):
    alist = []
    result.append(str(EE(i+2)))
print("\n".join(result + result[:-1][::-1]))


Fixed submission:
import math
import sys
K, N = [int(i) for i in input().split(' ')]
mod = 998244353
sys.setrecursionlimit(100000)

def mul(a, b):
    return ((a % mod) * (b % mod)) % mod

def cmb_f(n, r, mod):
#    print(n, r)
    if ( r<0 or r>n ):
        return 0
    r = min(r, n-r)
#    print(g1[n] * g2[r] * g2[n-r] % mod)
    return g1[n] * g2[r] * g2[n-r] % mod

NNN = 10**4
g1 = [1, 1]
g2 = [1, 1]
inverse = [0, 1]

for i in range( 2, NNN + 1 ):
    g1.append( ( g1[-1] * i ) % mod )
    inverse.append( ( -inverse[mod % i] * (mod//i) ) % mod )
    g2.append( (g2[-1] * inverse[-1]) % mod )

def EN(i):
    k2 = int((K - abs(K - int((i-1)/2) * 2) )/2)
    k1 = K - k2*2 - (1 if i % 2 == 0 else 0)
    result = 0
    for j in range(k2+1):
        if N < j:
            break
        result = (result + mul(mul(cmb_f(k2, j, mod) , cmb_f(N+k1-1, j+k1-1, mod)) , pow(2, j) % mod))% mod
    if i % 2 == 1:
        return result
    for j in range(k2+1):
        if N-1 < j:
            break
        result = (result + mul(mul(cmb_f(k2, j, mod), cmb_f(N+k1-2, j+k1-1, mod)), pow(2, j) % mod))% mod
    return result

if K == 1:
    print(0)
else:
    result = []
    for i in range(K):
        result.append(str(EN(i+2)))
    print("\n".join(result + result[:-1][::-1]))