Hint For Project Euler Problem 106 - Special Subset Sums - Meta Testing

Here is my hint for Project Euler Problem 106 - Special Subset Sums - Meta Testing.

Summary
function subsetSumsMetaTesting() {
  function factorial(num) {
    return num>1 ? factorial(num-1) * num : 1;
  }
  let n = 12;
  let factorials = Array(n+1).fill(1).map((e,i) => factorial(i));
  let result = 0;
  for (let k=2;k<=Math.floor(n/2);k++) {
    result += (0.5*(k-1)*factorials[n]/(factorials[k]**2*factorials[n-2*k]*(k+1)));
  }
  return result;
}

subsetSumsMetaTesting();

Hi, thanks for the solution suggestion. Can you add some comments explaining how the formula works?