When you are feeling inspired...

[angelscat]

...it is really uncomfortable to be bogged down by little details, such as the volume of an n dimensional sphere or the Stirling formula, isn't it? Well, I'll just record them here, once and for all:

vol(S^(n-1))=2*pi^(n/2)/Gamma(n/2)
log(n!) is approximately n*log(n)-n