Buggy python submission (verdict: Time Limit Exceeded):
from itertools import product, compress

N = int(input())
Ss = input()

Fss = [list(compress(Ss[:N], sels))[::-1] for sels in product([0, 1], repeat=N)]

ans = 0
for iFs in range(2 ** N):
    Fs = Fss[iFs]
    Gs = Fss[2 ** N - 1 - iFs]

    lenF = len(Fs)
    lenG = N - lenF
    dp = [1] + [0] * lenF
    for i, s in enumerate(Ss[N:], 1):
        dp2 = [0] * (lenF + 1)
        flg = False
        for j in range(lenF + 1):
            if 0 <= j-1 and s == Fs[j-1]:
                dp2[j] += dp[j-1]
            if 0 <= i-j-1 < lenG and s == Gs[i-j-1]:
                dp2[j] += dp[j]
            if dp2[j]:
                flg = True
        dp = dp2
        if not flg: break

    ans += dp[lenF]

print(ans)


Fixed submission:
from itertools import product, compress

N = int(input())
Ss = input()

Fss = [list(compress(Ss[:N], sels))[::-1] for sels in product([0, 1], repeat=N)]

ans = 0
for iFs in range(2 ** N):
    Fs = Fss[iFs]
    Gs = Fss[2 ** N - 1 - iFs]

    lenF = len(Fs)
    lenG = N - lenF
    dp = [1] + [0] * lenF
    for i, s in enumerate(Ss[N:]):
        dp2 = [0] * (lenF + 1)
        for j in range(lenF + 1):
            if dp[j] == 0: continue
            if j < lenF and s == Fs[j]:
                dp2[j+1] += dp[j]
            if 0 <= i-j < lenG and s == Gs[i-j]:
                dp2[j] += dp[j]
        dp = dp2

    ans += dp[lenF]

print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
from itertools import product, compress

N = int(input())
Ss = input()

Fss = [list(compress(Ss[:N], sels))[::-1] for sels in product([0, 1], repeat=N)]

ans = 0
for iFs in range(2 ** N):
    Fs = Fss[iFs]
    Gs = Fss[2 ** N - 1 - iFs]

    lenF = len(Fs)
    lenG = N - lenF
    dp = [1] + [0] * lenF
    for i, s in enumerate(Ss[N:], 1):
        dp2 = [0] * (lenF + 1)
        for j in range(lenF + 1)[::-1]:
            if 0 <= j-1 and s == Fs[j-1]:
                dp2[j] += dp[j-1]
            if 0 <= i-j-1 < lenG and s == Gs[i-j-1]:
                dp2[j] += dp[j]
        dp = dp2

    ans += dp[lenF]

print(ans)


Fixed submission:
from itertools import product, compress

N = int(input())
Ss = input()

Fss = [list(compress(Ss[:N], sels))[::-1] for sels in product([0, 1], repeat=N)]

ans = 0
for iFs in range(2 ** N):
    Fs = Fss[iFs]
    Gs = Fss[2 ** N - 1 - iFs]

    lenF = len(Fs)
    lenG = N - lenF
    dp = [1] + [0] * lenF
    for i, s in enumerate(Ss[N:]):
        dp2 = [0] * (lenF + 1)
        for j in range(lenF + 1):
            if dp[j] == 0: continue
            if j < lenF and s == Fs[j]:
                dp2[j+1] += dp[j]
            if 0 <= i-j < lenG and s == Gs[i-j]:
                dp2[j] += dp[j]
        dp = dp2

    ans += dp[lenF]

print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
from itertools import product, compress

N = int(input())
Ss = input()

ans = 0
for sels in product([0, 1], repeat=N):
    Fs = list(compress(Ss[:N], sels))[::-1]
    Gs = list(compress(Ss[:N], map(lambda x: 1-x, sels)))[::-1]

    lenF = len(Fs)
    lenG = N - lenF
    dp = [[0] * (lenF + 1) for i in range(N + 1)]
    dp[0][0] = 1
    for i, s in enumerate(Ss[N:], 1):
        for j in range(lenF + 1):
            if 0 <= j-1 and s == Fs[j-1]:
                dp[i][j] += dp[i-1][j-1]
            if 0 <= i-j-1 < lenG and s == Gs[i-j-1]:
                dp[i][j] += dp[i-1][j]

    ans += dp[N][lenF]

print(ans)


Fixed submission:
from itertools import product, compress

N = int(input())
Ss = input()

Fss = [list(compress(Ss[:N], sels))[::-1] for sels in product([0, 1], repeat=N)]

ans = 0
for iFs in range(2 ** N):
    Fs = Fss[iFs]
    Gs = Fss[2 ** N - 1 - iFs]

    lenF = len(Fs)
    lenG = N - lenF
    dp = [1] + [0] * lenF
    for i, s in enumerate(Ss[N:]):
        dp2 = [0] * (lenF + 1)
        for j in range(lenF + 1):
            if dp[j] == 0: continue
            if j < lenF and s == Fs[j]:
                dp2[j+1] += dp[j]
            if 0 <= i-j < lenG and s == Gs[i-j]:
                dp2[j] += dp[j]
        dp = dp2

    ans += dp[lenF]

print(ans)