The number of divisors of the central binomial coefficients

Rule

Each term is: Take the number of combinations of 2n things taken n at a time, then take the number of the divisors

Known as: The number of divisors of the central binomial coefficients

The first 15 terms (starting from n=1) are:

2 4 6 8 18 24 32 48 48 48 128 96 192 384 480

Example

To get the value for n=13:

  • Calculate the number of combinations of 2n things taken n at a time, giving 10400600.
  • Find the number's divisors, giving 1, 2, 4, 5, 7, 8, 10, 14, 17, 19, 20, 23, 25, 28, 34, 35, 38, 40, 46, 50, 56, 68, 70, 76, 85, 92, 95, 100, 115, 119, 133, 136, 140, 152, 161, 170, 175, 184, 190, 200, 230, 238, 266, 280, 322, 323, 340, 350, 380, 391, 425, 437, 460, 475, 476, 532, 575, 595, 644, 646, 665, 680, 700, 760, 782, 805, 850, 874, 920, 950, 952, 1064, 1150, 1190, 1288, 1292, 1330, 1400, 1564, 1610, 1615, 1700, 1748, 1900, 1955, 2185, 2261, 2300, 2380, 2584, 2660, 2737, 2975, 3059, 3128, 3220, 3230, 3325, 3400, 3496, 3800, 3910, 4025, 4370, 4522, 4600, 4760, 5320, 5474, 5950, 6118, 6440, 6460, 6650, 7429, 7820, 8050, 8075, 8740, 9044, 9775, 10925, 10948, 11305, 11900, 12236, 12920, 13300, 13685, 14858, 15295, 15640, 16100, 16150, 17480, 18088, 19550, 21850, 21896, 22610, 23800, 24472, 26600, 27370, 29716, 30590, 32200, 32300, 37145, 39100, 43700, 45220, 52003, 54740, 56525, 59432, 61180, 64600, 68425, 74290, 76475, 78200, 87400, 90440, 104006, 109480, 113050, 122360, 136850, 148580, 152950, 185725, 208012, 226100, 260015, 273700, 297160, 305900, 371450, 416024, 452200, 520030, 547400, 611800, 742900, 1040060, 1300075, 1485800, 2080120, 2600150, 5200300, 10400600
  • Count them, giving 192.

So the result is 192.