    n        count   n(n+1)(n+2)/6
    1            1               1  equal
    2            4               4  equal
    3           10              10  equal
    4           20              20  equal
    5           35              35  equal
    6           56              56  equal
   10          220             220  equal
  100       171700          171700  equal
  500     20958500        20958500  equal
