Data update

Task/Catalan-numbers/PascalABC.NET/catalan-numbers.pas

@@ -0,0 +1,25 @@
+##
+function binom(n, k: integer): int64;
+begin
+  result := 1;
+  for var i := 1 to k do
+    result := result * (n - i + 1) div i
+end;
+
+function catalan1(n: integer) := binom(2 * n, n) div (n + 1);
+
+function catalan2(n: integer): integer;
+begin
+  if n = 0 then begin result := 1; exit end;
+  for var i := 0 to n - 1 do
+    result += catalan2(i) * catalan2(n - 1 - i)
+end;
+
+function catalan3(n: integer): integer;
+begin
+  if n > 0 then result := 2 * (2 * n - 1) * catalan3(n - 1) div (1 + n)
+  else result := 1;
+end;
+
+for var i := 0 to 15 do
+  writeln(i:2, catalan1(i):9, catalan2(i):9, catalan3(i):9);