June 2018 Update

Task/Catalan-numbers-Pascals-triangle/00DESCRIPTION

@@ -3,9 +3,10 @@ Print out the first   '''15'''   Catalan numbers by extracting them fr
 
 
 ;See:
-* &nbsp; [http://milan.milanovic.org/math/english/fibo/fibo4.html Catalan Numbers and the Pascal Triangle]. &nbsp; &nbsp; This method enables calculation of Catalan Numbers using only addition and subtraction. <br> &nbsp; &nbsp; '''The (above) link is broken.'''
+* &nbsp; [https://archive.is/0IrNp Catalan Numbers and the Pascal Triangle]. <!-- Relation Pascal Triangle and the Catalan Numbers Radoslav Jovanovic --> &nbsp; &nbsp; This method enables calculation of Catalan Numbers using only addition and subtraction.
+<!-- '''http://milan.milanovic.org/math/english/fibo/fibo4.html is broken. -->
 * &nbsp; [http://mathworld.wolfram.com/CatalansTriangle.html Catalan's Triangle] for a Number Triangle that generates Catalan Numbers using only addition.
-
+* &nbsp; Sequence [http://oeis.org/A000108 A000108] on OEIS has a lot of information on Catalan Numbers.
 
 ;Related Tasks:
 [[Pascal's triangle]]

Task/Catalan-numbers-Pascals-triangle/Factor/catalan-numbers-pascals-triangle.factor

@@ -0,0 +1,14 @@
+USING: arrays grouping io kernel math prettyprint sequences ;
+IN: rosetta-code.catalan-pascal
+
+: next-row ( seq -- seq' )
+    2 clump [ sum ] map 1 prefix 1 suffix ;
+
+: pascal ( n -- seq )
+    1 - { { 1 } } swap [ dup last next-row suffix ] times ;
+
+15 2 * pascal [ length odd? ] filter [
+    dup length 1 = [ 1 ]
+    [ dup midpoint@ dup 1 + 2array swap nths first2 - ] if
+    pprint bl
+] each drop

Task/Catalan-numbers-Pascals-triangle/Go/catalan-numbers-pascals-triangle.go

@@ -0,0 +1,18 @@
+package main
+
+import "fmt"
+
+func main() {
+    const n = 15
+    t := [n + 2]uint64{0, 1}
+    for i := 1; i <= n; i++ {
+        for j := i; j > 1; j-- {
+            t[j] += t[j-1]
+        }
+        t[i+1] = t[i]
+        for j := i + 1; j > 1; j-- {
+            t[j] += t[j-1]
+        }
+        fmt.Printf("%2d : %d\n", i, t[i+1]-t[i])
+    }
+}

Task/Catalan-numbers-Pascals-triangle/OCaml/catalan-numbers-pascals-triangle.ocaml

@@ -0,0 +1,12 @@
+let catalan : int ref = ref 0 in
+Printf.printf "%d ," 1 ;
+for i = 2 to 9  do
+let nm : int ref = ref 1 in
+let den : int ref = ref 1 in
+for k = 2 to i do
+nm := (!nm)*(i+k);
+den := (!den)*k;
+catalan := (!nm)/(!den) ;
+done;
+print_int (!catalan); print_string "," ;
+done;;

Task/Catalan-numbers-Pascals-triangle/Oforth/catalan-numbers-pascals-triangle.oforth

@@ -1,2 +1,7 @@
-: pascal(n)  [ 1 ] #[ dup 0 + 0 rot + zipWith(#+) ] times(n) ;
-: catalan(n)  pascal(n 2 * ) at(n 1+) n 1+ / ;
+import: mapping
+
+: pascal( n -- [] )
+   [ 1 ] n #[ dup [ 0 ] + [ 0 ] rot + zipWith( #+ ) ] times ;
+
+: catalan( n -- m )
+   n 2 * pascal at( n 1+ ) n 1+ / ;

Task/Catalan-numbers-Pascals-triangle/Scala/catalan-numbers-pascals-triangle.scala

@@ -0,0 +1,5 @@
+def catalan(n: Int): Int =
+  if (n <= 1) 1
+  else (0 until n).map(i => catalan(i) * catalan(n - i - 1)).sum
+
+(1 to 15).map(catalan(_))