feat: add Catalan number algorithm

Maths/CatalanNumber.js

@@ -0,0 +1,25 @@
+/**
+ * @function catalanNumber
+ * @description Catalan numbers are a sequence of natural numbers with
+ *   many applications in combinatorics. The nth Catalan number is given
+ *   by: C(n) = (2n)! / ((n+1)! * n!)
+ * @param {number} n - A non-negative integer
+ * @returns {number} - The nth Catalan number
+ * @see https://en.wikipedia.org/wiki/Catalan_number
+ * @example catalanNumber(0) => 1
+ * @example catalanNumber(3) => 5
+ * @example catalanNumber(5) => 42
+ */
+const catalanNumber = (n) => {
+  if (!Number.isInteger(n) || n < 0) {
+    throw new TypeError('Input must be a non-negative integer')
+  }
+  if (n === 0 || n === 1) return 1
+  let result = 0
+  for (let i = 0; i < n; i++) {
+    result += catalanNumber(i) * catalanNumber(n - 1 - i)
+  }
+  return result
+}
+
+export { catalanNumber }

Maths/test/CatalanNumber.test.js

@@ -0,0 +1,39 @@
+import { catalanNumber } from '../CatalanNumber.js'
+
+describe('catalanNumber', () => {
+  test('catalanNumber(0) returns 1', () => {
+    expect(catalanNumber(0)).toBe(1)
+  })
+
+  test('catalanNumber(1) returns 1', () => {
+    expect(catalanNumber(1)).toBe(1)
+  })
+
+  test('catalanNumber(2) returns 2', () => {
+    expect(catalanNumber(2)).toBe(2)
+  })
+
+  test('catalanNumber(3) returns 5', () => {
+    expect(catalanNumber(3)).toBe(5)
+  })
+
+  test('catalanNumber(4) returns 14', () => {
+    expect(catalanNumber(4)).toBe(14)
+  })
+
+  test('catalanNumber(5) returns 42', () => {
+    expect(catalanNumber(5)).toBe(42)
+  })
+
+  test('catalanNumber(6) returns 132', () => {
+    expect(catalanNumber(6)).toBe(132)
+  })
+
+  test('throws TypeError for negative input', () => {
+    expect(() => catalanNumber(-1)).toThrow(TypeError)
+  })
+
+  test('throws TypeError for float input', () => {
+    expect(() => catalanNumber(1.5)).toThrow(TypeError)
+  })
+})