You can simplify the calculation to

sub NwithM {
    my $f = 4-1;
    my( $L, $M ) = @_;
    my $T=1;
    my $tmp = 1;
    for my $m ( 1 .. $M ) {
        $tmp *= ($L-$m+1)/$m*$f;
        $T += $tmp;
    }
    return $T;
}
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