Correctness of derivnum(X=1/2,zeta(X),41)

[Georgi Guninski <gguninski@gmail.com>]

On mathoverflow [1] there is conjecture about the nearest integer to
[zeta^(k)(1-1/B)]=-B^(k+1)*factorial(k)

Answer of controversial theoretic result claims the explicit
numerical counterexample k=41,B=2

I couldn't compute the counterexample on mpmath with high precision
due to internal error, but pari agrees the counterexample is correct:

K=41;B=2;T=derivnum(X=1-1/B,zeta(X),K);(round(T)+B^(K+1)*factorial(K))
%16 = 3.00....

Is it plausible that the pari computation is correct with high (what?)
precision?

What other CAS say about it?

[1]: https://mathoverflow.net/questions/404779/on-the-nearest-integer-to-zetak1-1-b-b-ge-2