quantum_kick.py

from sympy import sqrt

N = 15
a = [[]]*N
for n in range(N):
    a[n] = [0]*(n+1)
    if n == 0:
        a[0][0] = 1
    else:
        for l in range(n + 1):
            A = a[n-1][l+1] * sqrt(l+1) if l + 1 <= n - 1 else 0
            B = a[n-1][l-1] * sqrt(l) if l - 1 >= 0 else 0
            a[n][l] = A + B

for n in range(N):
    print(a[n])