I realise this is only a surface level comparison but the Julia code uses the built in factorial function which I think uses lookup tables and the C# version us

I realise this is only a surface level comparison but the Julia code uses the built in factorial function which I think uses lookup tables and the C# version uses a recursive static method, the Python code has your own lookup table. I guess that’s on the hot path? I haven’t taken the time to check if you’ve put a lookup or memoized it somewhere.