#!/home/ben/software/install/bin/perl
use warnings;
use strict;
use Math::Trig;

my $factorial = 1;
my $e = exp (1.0);
# This is the format for printing out the numbers used in "sprintf"
# below.
my $format = "<tr><td>%3d</td>" . ("<td>%10g</td>" x 5) . "</tr>\n";

for my $n (1..50) {
    $factorial *= $n;
    # Wikipedia's formula for Stirling's Approximation.
    my $stirling = sqrt (2*pi*$n) * ($n/$e)**$n;
    my $ratio = $factorial / $stirling;
    # David MacKay's "Stirling's Approximation".
    my $mackay = $n**$n * exp (-$n);
    my $mratio = $factorial / $mackay;
    # This is the output string.
    my $out = sprintf $format, $n, $factorial, $stirling, $ratio, $mackay, $mratio;
    # This converts the e+12-format output into HTML format.
    $out =~ s!e\+0*(\d+)!&times;10<sup>$1</sup>!g;
    print "$out";
}