# -*- coding: utf-8 -*-
"""
Created on Fri Jun 14 21:32:38 2024

@author: franc
"""
import matplotlib.pyplot as plt

# Question 1
def a(n):
    if n==0:
        return 1
    else:
        return (2*n-1)/2/n*a(n-1)
        
# Question 2
def S(n,x):
    s=0
    for k in range(n+1):
        s+=a(k)*x**k
    return s
    
print()
print()
print('en bleu: la suite (a_n)')
print()
print('en vert, la suite (2S_n(-1))')
# Question 3
lx=[k for k in range(11)]
ly=[a(k) for k in range(11)]
plt.plot(lx,ly)


# Question 4
lx=[k for k in range(31)]
ly=[2*S(n,-1) for n in range(31)]
plt.plot(lx,ly)