Two problems.
1.

sub factorial
{
  my $n = @_;
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This forces the @_ array to be evaluated in a scalar context. An array evaluated in a scalar context produces the length of the array. Useful - but not what you want in this case!

Change it to:
my ($n) = @_;

2.  my $exp = ($n/exp(1))^$n;
'^' is the bitwise XOR operator in perl.

Change to:
  my $exp = ($n/exp(1))**$n;

Actually there may be a third problem. I kicked this off before writing this response. My (admittedly lame) PC has been maxed out since.