"""
Bernoulli Zahlen
(c) Jürgen Meier
www.3d-meier.de
10.10.2024
"""

import math


B0 = 1.0 
B1 = -1/2.0 
B2 = 1/6.0 
B3 = 0.0
B4 = -1/30.0 
B5 = 0
B6 = 1/42.0 
B7 = 0
B8 = -1/30.0 
B9 = 0
B10 = 5/66.0 
B11 = 0
B12 = -691/2730.0
B13 = 0
B14 = 7/6.0 
B15 = 0
B16 = -3617/510.0 
B17 = 0
B18 = 43867/798.0 
B19 = 0
B20 = -174611/330.0 
B21 = 0
B22 = 854513/138.0 
B23 = 0
B24 = -236364091/2730.0 
B25 = 0
B26 = 8553103/6.0 
B27 = 0
B28 = -23749461029/870.0 
B29 = 0
B30 = 8615841276005/14322.0 
B31 = 0
B32 = -7709321041217/510.0
B33 = 0
B34 = 2577687858367/6.0
B35 = 0
B36 = -26315271553053477373/1919190.0
B37 = 0
B38 = 2929993913841559/6.0
B39 = 0
B40 = -261082718496449122051/13530.0
B41 = 0
B42 = 1520097643918070802691/1806.0
B43 = 0
B44 = -27833269579301024235023/690.0
B45 = 0
B46 = 596451111593912163277961/282.0
B47 = 0
B48 = -5609403368997817686249127547/46410.0
B49 = 0
B50 = 495057205241079648212477525/66.0
B51 = 0
B52 = -801165718135489957347924991853/1590.0
B53 = 0
B54 = 29149963634884862421418123812691/798.0
B55 = 0
B56 = -2479392929313226753685415739663229/870.0
B57 = 0
B58 = 84483613348880041862046775994036021/354.0
B59 = 0
B60 = -1215233140483755572040304994079820246041491/56786730.0
B61 = 0
B62 = 12300585434086858541953039857403386151/6.0
B63 = 0
B64 = -106783830147866529886385444979142647942017/510.0
B65 = 0
B66 = 1472600022126335654051619428551932342241899101/64722.0
B67 = 0
B68 = -78773130858718728141909149208474606244347001/30.0

Bernoulli = [B0, B1, B2, B3, B4, B5, B6, B7, B8, B9, B10, B11, B12, B13, B14, B15, B16, B17, B18, B19, B20, B21, B22, B23, B24, B25, B26, B27, B28, B29, B30, B31, B32, B33, B34, B35, B36, B37, B38, B39, B40, B41, B42, B43, B44, B45, B46, B47, B48, B49, B50, B51, B52, B53, B54, B55, B56, B57, B58, B59, B60, B61, B62, B63, B64, B65, B66, B67, B68]

x = 0.5
a = 0

for i in range(0, 68):
    a = a + Bernoulli[i]*(x**i)/math.factorial(i)

print(a)
print(x/(math.exp(x)-1))