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I run the AWK code and I get
The factorial of 200 is inf
This suggests me that AWK does not use the same int IEEE-standard -module as Python.
It seems that AWK’s limit is 170!.
How can you make AWK understand as large integers as Python?
From here:
Python can have integers of any length, depending on available memory. This is independent of IEEE 754. BTW, that standard gives the limit of a double precision float at about 10^(+/-308). The value of log10(factorial(171)) is > 309. See also Double Precision and What Every Scientist Should Know About Floating-Point Arithmetic.