import numpy as np
import math
import matplotlib.pyplot as plt

# Coefficients du binôme
b=np.zeros([13, 13])
for i in range(13):
    b[i, 0] = 1
for i in range(1, 13):
    for j in range(1, 13):
        b[i, j] = b[i - 1, j - 1]+ b[i - 1, j]

print(b)

# Calcul de A_0,...,A_12
A=[1, 1]
for n in range(2, 13):
    s = 0
    for j in range(n):
        s+=b[n - 1, j]*A[j]
        A.append(s)

print(A)

# Courbe
def f(x):
    s=0
    for i in range(13):
        s+=x**i*A[i]/math.factorial(i)
    return(s)

T=np.arange(-0.99,1,0.01)
X=f(T)
plt.plot(T,X)
plt.show()