"""
Berechnung von Zeta(3)
(c) Jürgen Meier
www.3d-meier.de
05.07.2024
"""

import math


p = 0
k = 3
for n in range(0, k + 1):
    a = 5265*n**4+13878*n**3+13761*n**2+6120*n+1040
    zaehler = ((-1.0)**n)*a*(math.factorial(n)**2)* math.factorial(2*n)
    nenner = (4*n+1)* (4*n+3)*(n+1)* (3*n+1)* (3*n+1)* (3*n+2)* (3*n+2)* math.factorial(4*n)

    p = p + zaehler/nenner

print(p/72)