Add Catalan number (#5846)

src/main/java/com/thealgorithms/maths/CatalanNumbers.java

@@ -0,0 +1,39 @@
+package com.thealgorithms.maths;
+
+/**
+ * Calculate Catalan Numbers
+ */
+public final class CatalanNumbers {
+    private CatalanNumbers() {
+    }
+
+    /**
+     * Calculate the nth Catalan number using a recursive formula.
+     *
+     * @param n the index of the Catalan number to compute
+     * @return the nth Catalan number
+     */
+    public static long catalan(final int n) {
+        if (n < 0) {
+            throw new IllegalArgumentException("Index must be non-negative");
+        }
+        return factorial(2 * n) / (factorial(n + 1) * factorial(n));
+    }
+
+    /**
+     * Calculate the factorial of a number.
+     *
+     * @param n the number to compute the factorial for
+     * @return the factorial of n
+     */
+    private static long factorial(final int n) {
+        if (n == 0 || n == 1) {
+            return 1;
+        }
+        long result = 1;
+        for (int i = 2; i <= n; i++) {
+            result *= i;
+        }
+        return result;
+    }
+}