I'm trying to calculate entropies for an absolutely giant system by counting states, and this means I have to use some obscenely large numbers. I'm running
Nn = 5*10^20 - 1.381 * 10^-23 Log[Multinomial[Nn/3, Nn/3, Nn/3]]
and (of COURSE) it comes out to an obscenely large number. Honestly, I would be alright with just the order of magnitude without having to do each factorial estimation separately by hand... Are there any little tricks to getting around this
Overflow? I'm sure Mathematica has some workarounds for avoiding machine precision errors.... there's no way this number is eating all my 8 gigs of ram.
For reference, the output of