Catalan numbers/Pascal's triangle

The task is to print out the first 15 Catalan numbers by extracting them from Pascal's triangle, see Catalan Numbers and the Pascal Triangle.

Catalan numbers/Pascal's triangle
You are encouraged to solve this task according to the task description, using any language you may know.

C++

<lang cpp>// Generate Catalan Numbers // // Nigel Galloway: June 9th., 2012 //

1. include <iostream>

int main() {

 const int N = 15;
 int t[N+2] = {0,1};
 for(int i = 1; i<=N; i++){
   for(int j = i; j>1; j--) t[j] = t[j] + t[j-1];
   t[i+1] = t[i];
   for(int j = i+1; j>1; j--) t[j] = t[j] + t[j-1];
   std::cout << t[i+1] - t[i] << " ";
 }
 return 0;

}</lang>

Produces:

1 2 5 14 42 132 429 1430 4862 16796 58786 208012 742900 2674440 9694845

D

Translation of: C++

<lang d>void main() {

   import std.stdio;

   enum uint N = 15;
   uint[N + 2] t;
   t[1] = 1;

   foreach (immutable i; 1 .. N + 1) {
       foreach_reverse (immutable j; 2 .. i + 1)
           t[j] = t[j] + t[j - 1];
       t[i + 1] = t[i];
       foreach_reverse (immutable j; 2 .. i + 2)
           t[j] = t[j] + t[j - 1];
       write(t[i + 1] - t[i], ' ');
   }

}</lang>

Output:

1 2 5 14 42 132 429 1430 4862 16796 58786 208012 742900 2674440 9694845 

Perl 6

<lang perl6>constant @pascal = [1], -> @p { [0, @p Z+ @p, 0] } ... *;

constant @catalan = gather for 2, 4 ... * -> $ix {

   my @row := @pascal[$ix];
   my $mid = +@row div 2;
   take [-] @row[$mid, $mid+1]

}

.say for @catalan[^20];</lang>

Output:

1
2
5
14
42
132
429
1430
4862
16796
58786
208012
742900
2674440
9694845
35357670
129644790
477638700
1767263190
6564120420

Run BASIC

<lang runbasic>n = 15 dim t(n+2) t(1) = 1 for i = 1 to n

 for  j = i to 1 step -1  : t(j) = t(j) + t(j-1): next j
 t(i+1) = t(i)
 for  j = i+1 to 1 step -1: t(j) = t(j) + t(j-1 : next j

print t(i+1) - t(i);" "; next i</lang>

Output:

1 2 5 14 42 132 429 1430 4862 16796 58786 208012 742900 2674440 9694845 

Tcl

<lang tcl>proc catalan n {

   set result {}
   array set t {0 0 1 1}
   for {set i 1} {[set k $i] <= $n} {incr i} {

for {set j $i} {$j > 1} {} {incr t($j) $t([incr j -1])} set t([incr k]) $t($i) for {set j $k} {$j > 1} {} {incr t($j) $t([incr j -1])} lappend result [expr {$t($k) - $t($i)}]

   }
   return $result

}

puts [catalan 15]</lang>

Output:

1 2 5 14 42 132 429 1430 4862 16796 58786 208012 742900 2674440 9694845