Problem:
 Score : 600 points    Problem Statement Let us define the oddness of a permutation p = { p_1,\ p_2,\ ...,\ p_n } of { 1,\ 2,\ ...,\ n } as \sum_{i = 1}^n |i - p_i| .  Find the number of permutations of { 1,\ 2,\ ...,\ n } of oddness k , modulo 10^9+7 .      Constraints  All values in input are integers.  1 \leq n \leq 50  0 \leq k \leq n^2         Input Input is given from Standard Input in the following format:  n  k       Output Print the number of permutations of { 1,\ 2,\ ...,\ n } of oddness k , modulo 10^9+7 .        Sample Input 1 3 2      Sample Output 1 2  There are six permutations of { 1,\ 2,\ 3 }. Among them, two have oddness of 2 :  { 2,\ 1,\ 3 } and { 1,\ 3,\ 2 }.       Sample Input 2 39 14      Sample Output 2 74764168

Solution (Python):
import sys

MOD = 10**9 + 7

N, K = map(int, input().split())

maxS = N*N//2
if K > maxS or K%2:
    print(0)
    sys.exit()

dp = [[0]*(maxS+1) for j in range(N+1)]
dp[0][0] = 1
for i in range(1, N+1):
    dp2 = [[0]*(maxS+1) for j in range(N+1)]
    for j in range(i+1):
        for s in range(0, maxS+1, 2):
            s0 = s-2*j
            if s0 < 0: continue
            dp2[j][s] = (2*j+1)*dp[j][s0]
            if j+1 <= N:
                dp2[j][s] += (j+1)*(j+1)*dp[j+1][s0]
            if j-1 >= 0:
                dp2[j][s] += dp[j-1][s0]
            dp2[j][s] %= MOD
    dp = dp2

print(dp[0][K])

Solution (Python):
N, K = map(int, input().split())
MOD = 10 ** 9 + 7
dp = [[[0] * 2600 for i in range(N + 5)] for j in range(N + 5)]
dp[0][0][0] = 1

for i in range(N):
    for j in range(N + 1):
        for k in range(K + 1):
            if dp[i][j][k] == 0:
                continue
            a = k + 2 * j
            dp[i + 1][j][a] += dp[i][j][k]
            dp[i + 1][j][a] += dp[i][j][k] * j
            if j > 0:
                dp[i + 1][j - 1][a] += dp[i][j][k] * j * j
            dp[i + 1][j][a] += dp[i][j][k] * j
            dp[i + 1][j + 1][a] += dp[i][j][k]
            dp[i + 1][j][a] %= MOD
            dp[i + 1][j - 1][a] %= MOD
            dp[i + 1][j + 1][a] %= MOD

print(dp[N][0][K])