use strict;
use warnings;

use List::Util qw( sum );

{
   my %memoize;

   sub calcIt {
      my ($n, $d) = @_;
      return $memoize{"$n:$d"} ||= (
         ($d
            ? sum map { calcIt($_, $d-1) } 1..$n
            : $n * ( $n + 1 ) / 2
         )
      );
   }
}

{
   my $N = 20;
   my $D = 7;

   print('$n\\$d');
   for my $d (1..$D) {
      print("\t$d");
   }
   print("\n");

   for my $n (1..$N) {
      print("$n");
      for my $d (1..$D) {
         print("\t", calcIt($n, $d));
      }
      print("\n");
   }
}