from fractions import Fraction

coefs = [
    Fraction(1),
    Fraction(1),
    Fraction(1,2),
    Fraction(35, 216),
    Fraction(65, 1728),
    Fraction(17, 2592),
    Fraction(41, 46656),
    Fraction(17,186624),
    Fraction(65, 8957952),
    Fraction(35, 80621568),
    Fraction(1, 53747712),
    Fraction(1, 1934917632),
    Fraction(1, 139314069504),
]

from math import factorial
ev = 0
for i, coef in enumerate(coefs):
    ev += factorial(i) * coef

print ev
# 4084571/559872