import numberdb.sage as numberdb
from sage.rings.real_arb import RealBallField
from math import comb

def c(k, digits=100):
    F = RealBallField(numberdb.bits(digits, losing=k+80))
    return sum(((-1)**j * comb(k,j) / F(2*j+2).zeta()
                for j in range(k+1)), F(0))

[c(k) for k in range(257)]