loga1 = log(a2*a3*.*an/n!)
a1 = a2*a3*.*an/n!
a1 = a2*a3*.*a(n-1)/(n-1)!
==> 1 = (an/n!)/(a(n-1)/(n-1)!)
==> an = na(n-1)
==> an = a1*n!