# -*- coding: utf-8 -*-
"""
Created on Fri Jun 12 09:10:25 2026

@author: François Coulombeau
"""
def fact(n):
    res = 1
    for k in range(n):
        res *= (k+1)
    return res

S = 0
N = 30
for k in range(N):
    S += k**k/fact(2*k)

import numpy as np
print(np.exp(1/2),S, (np.exp(1)+1)/2)