#!/usr/bin/perl
use warnings;
use strict;

open my $OUT, '>', 'output.txt' or die "output.txt: $!";

for my $file (glob '*.txt') {
    open my $FH, '<', $file or die "$file: $!";
    while (<$FH>) {
        print {$OUT} $_ unless 1 == $.;
    }
}
close $OUT or die $!;