## Number of plane rational plane curves
## of degree d>=1 going through 3d-1 points

def K_(d):
    L = [1]
    for j in range(1,d):
        L = update(L)
    return L

def update(A):
    m = len(A)+1
    b = 0
    for k in range(1,m):
        h = m-k
        n = 3*m-4; d = 3*k-2
        bp = k*h*binom(n,d)
        bn = k**2*bp*(n-d)//(d+1)
        b += A[k-1]*A[h-1]*(k*h*bp-bn)
    return A +[b]

def binom(n,m):
    b = 1
    for j in range(m):
        b *= n-j
    for j in range (1,m+1):
        b //=j
    return b
    
print(K_(10))

'''
[1, 1, 12, 620, 87304, 26312976, 14616808192, 13525751027392, 19385778269260800, 40739017561997799680]
'''