References on Taylor series expansion of Riemann xi function

In the paper:

M. W. Coffey, "Asymptotic estimation of $\xi^{(2n)}(1/2)$: On a conjecture of Farmer and Rhoades", Mathematics of Computation, {\bf 78} (2009) 1147--1154

you may find the first terms of an asymptotic expansion for $\log\xi^{(2n)}(1/2)$. From it you may get a good estimate of the coefficients $a_{2n}$.

In particular

$$\log a_{2n}=2[1-\log(4n)+\log(\log n)]n-\frac{2n}{\log n}+\frac74\log(2n)-\frac34\log(\log n)+O(1)$$

An accurate asymptotic estimate for the Taylor coefficients was obtained via the saddle point method in

Griffin+Ono+Rolen+Zagier, Jensen polynomials for the Riemann zeta function and other sequences - arXiv 1902.07321 www.pnas.org/cgi/doi/10.1073/pnas.1902572116

A short verification of the asymptotic formula was posted to the Pari/GP users mailing list, with references

Learning with GP: Griffin,Ono,Rolen,Zagier asymptotic formula for xi(s) http://pari.math.u-bordeaux.fr/archives/pari-users-1908/msg00022.html

J. Gélinas