Partition and Sequence Counter

/**
 * Computes the number of ways to partition n elements into k non-empty subsets.
 *
 * @param {number} n - The total number of elements
 * @param {number} k - The number of non-empty subsets
 * @returns {number} The count of ways to partition n into k subsets
 * @throws {Error} If n or k is negative, or if k > n
 */
function countSetPartitions(n, k) {
  // IMPLEMENTATION HERE
}

/**
 * Computes the total number of ways to partition n elements.
 *
 * @param {number} n - The total number of elements
 * @returns {number} The total count of partitions
 * @throws {Error} If n is negative
 */
function countTotalPartitions(n) {
  // IMPLEMENTATION HERE
}

/**
 * Computes the number of structurally different binary trees with n nodes.
 *
 * @param {number} n - The number of nodes
 * @returns {number} The count of distinct binary tree structures
 * @throws {Error} If n is negative
 */
function countBinaryTrees(n) {
  // IMPLEMENTATION HERE
}

module.exports = {
  countSetPartitions,
  countTotalPartitions,
  countBinaryTrees,
};