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

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

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