log(n!) = log(1) + log(2) + ... + log(n)
        = 1/2 log(1) + (log(1) + log(2))/2
                     + (log(2) + log(3))/2
                     + ...
                     + (log(n-1) + log(n))/2
                     + 1/2 log(n)

##</code><code>##

log(n!) = 1/2 0 + Integral from 1 to n of log(x) +
          1/2 log(n) + e(1) + e(2) + ... + e(n-1)

##</code><code>##

log(n!) = 1/2 0 + Integral from 1 to n of log(x) +
          1/2 log(n) + e(1) + e(2) + ... + e(n-1)
        = n*log(n) - n + 1 - 1/2 log(n)
          + (e(1) + e(2) + e(3) + ...)
          - (e(n) + e(n+1) + e(n+2) + ...)
        = n*log(n) - n + log(n)/2 + E + 1
          - e(n) - e(n+1) - e(n+2) - ...

##</code><code>##

n! = K * sqrt(n) + n**n * (1 + O(1/n)) / e**n