Implement a function to compute the nth Catalan number

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;
+    }
+}

src/test/java/com/thealgorithms/maths/CatalanNumbersTest.java

@@ -0,0 +1,33 @@
+package com.thealgorithms.maths;
+
+import static org.junit.jupiter.api.Assertions.assertAll;
+import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertThrows;
+
+import org.junit.jupiter.api.Test;
+
+/**
+ * Test class for CatalanNumbers
+ */
+class CatalanNumbersTest {
+
+    @Test
+    void testCatalanNumbers() {
+        assertEquals(1, CatalanNumbers.catalan(0)); // C(0) = 1
+        assertEquals(1, CatalanNumbers.catalan(1)); // C(1) = 1
+        assertEquals(2, CatalanNumbers.catalan(2)); // C(2) = 2
+        assertEquals(5, CatalanNumbers.catalan(3)); // C(3) = 5
+        assertEquals(14, CatalanNumbers.catalan(4)); // C(4) = 14
+        assertEquals(42, CatalanNumbers.catalan(5)); // C(5) = 42
+        assertEquals(132, CatalanNumbers.catalan(6)); // C(6) = 132
+        assertEquals(429, CatalanNumbers.catalan(7)); // C(7) = 429
+        assertEquals(1430, CatalanNumbers.catalan(8)); // C(8) = 1430
+        assertEquals(4862, CatalanNumbers.catalan(9)); // C(9) = 4862
+        assertEquals(16796, CatalanNumbers.catalan(10)); // C(10) = 16796
+    }
+
+    @Test
+    void testIllegalInput() {
+        assertAll(() -> assertThrows(IllegalArgumentException.class, () -> CatalanNumbers.catalan(-1)), () -> assertThrows(IllegalArgumentException.class, () -> CatalanNumbers.catalan(-5)));
+    }
+}