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.