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Help summing an infinite series

I have been trying to evaluate the following series using SageMath.

 sum((x^x)/(factorial(x)*exp(x)) - 1/sqrt(2*pi*x), x, 1, +oo).n()

The answer should be -0.084069508727655... (-2/3 - zeta(1/2)/sqrt(Pi)), but I get the following error when the upper limit is above 96:

RuntimeError: maximum recursion depth exceeded while calling a Python object

Is there any way SageMath could give me even the first few digits of the infinite sum? This sum seems to evaluate just fine in Maple and Mathematica, but not in any open source program I have tried, including Axiom, Maxima, PARI, and SymPy.

Any help would be greatly appreciated.