Re: recursive formula.

[rsteinke]

Should be something like

sub p
{
    my @args = @_; # for clarity, more efficient not to copy

    # initializing this handles the zero argument case
    my $result = 0;

    $result += ($args[$_] - ($_ ? $args[$_-1] : 0))
        * p(@args[0..($_-1)],@args[($_+1)..(@args-1)])
            foreach(0..(@args-1));

    return $result;
}

note: untested