Data update

Task/Catalan-numbers/PARI-GP/catalan-numbers-6.parigp

@@ -0,0 +1 @@
+Vec((1-sqrt(1 - 4*x))/(2*x)+O(x^16))

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);

Task/Catalan-numbers/Rust/catalan-numbers-2.rs

@@ -0,0 +1,33 @@
+struct Catalan {
+    catalans: Vec<i64>,
+    n: i64,
+}
+
+impl Default for Catalan {
+    fn default() -> Self {
+        Catalan {
+            catalans: vec![1],
+            n: 1,
+        }
+    }
+}
+
+impl Iterator for Catalan {
+    type Item = i64;
+
+    fn next(&mut self) -> Option<Self::Item> {
+        let c = *self.catalans.last().unwrap();
+        let next = 2 * c * (2 * self.n - 1) / (self.n + 1);
+
+        self.catalans.push(next);
+        self.n += 1;
+
+        Some(next)
+    }
+}
+
+fn main() {
+    for (i, catalan) in Catalan::default().take(15).enumerate() {
+        println!("c_n({}) = {}", i, catalan);
+    }
+}