"""
Werte der Bernoulli Konstante
(c) Jürgen Meier
www.3d-meier.de
10.10.2024
"""

import math
import decimal


# Anzahl Kommastellen
decimal.getcontext().prec = 250

a1 = decimal.Decimal(-1)

n = 20

b = 0
    
for k in range(0, n+1):
    a = 0 
    for j in range(0, k+1):    
        d1 = decimal.Decimal(str(math.factorial(k)))
        d2 = decimal.Decimal(str(j**n))
        d3 = decimal.Decimal(str(math.factorial(j)))
        d4 = decimal.Decimal(str( math.factorial(k-j)))
        a = a + ((a1**j) * d1 * d2)/(d3 * d4)

    b = b + a/(k + 1)

print(b)