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binomial coefficient  and  untouchable n.

First numbers that belong to both sets:

120, 210, 276, 406, 792, 1128, 1326, 1596, 1716, 1820, 1830, 2024, 2600, 2628, 2850, 3060, 3276, 3432, 3486, 3828, 3876, 4368, 5456, 5778, 5886, 6188, 6216, 7140, 7260, 7750, 7770, 8008, 8568, 8778, 9180, 9880, 10296, 10440, 10626, 11480, 11628, 12880, 13530, 14190, 14706, 15400, 15504, 16836, 17550, 17766, 18336, 19110, 20100, 20910, 21528, 22100, 23436, 24804, 25200, 25878, 26334, 27720, 27966, 28680, 28920, 29646, 30628, 30876, 32640, 33670, 34716, 34980, 35778, 35960, 35990, 36046, 37128, 38226, 38760, 39060, 41328, 41616, 41664, 42504, 43758, 44850, 47586, 48516, 52360, 53628, 53956, 54264, 57970, 59640, 60726, 61776, 62196, 64620, 64824, 64980, 66066, 67528, 69006, 70500, 72390, 73536, 75582, 76076, 81406, 82160, 83028, 83436, 84666, 85320, 86736, 87990, 88410, 88560, 90100, 91378, 95266, 95284, 98770, 98790, 102378, 103740, 104196, 107880, 111156, 111628, 113050, 115440, 119316, 122760, 123256, 125970, 126756, 127260, 131328, 134940, 135460, 137550, 139656, 142880, 143916, 146070, 150426, 154290, 159330, 161700, 163878, 165600, 170544, 170820, 174936, 177906, 179700, 180300, 182106, 185136, 187460, 190036, 194376, 194580, 196878, 200028, 201376, 201930, 202566, 203490, 204156, 207046, 209628, 210276, 214840, 215496, 217470, 223446, 225456, 226128, 227920, 228150, 228826, 231540, 233586, 237016, 237336, 239778, 241860, 242556, 244650, 250278, 253116, 256686, 258840, 259560, 260130, 261726, 264628, 265356, 266916, 276396, 277140, 278256, 280126, 282376, 283128, 286146, 294528, 297606, 298378, 300700, 301476, 303810, 304590, 306936, 307720, 310866, 313236, 322806, 324632, 330078, 332520, 333336, 335790, 336610, 339900, 341376, 343206, 346104, 346528, 355746, 357760, 359128, 359976, 362526, 363378, 365940, 372816, 374660, 376992, 383250, 386760, 391170, 392084, 393828, 394716, 397386, 400960, 404550, 405450, 408156, 411778, 412686, 415416, 423660, 437580, 438516, 442270, 446040, 447580, 448878, 449826, 453628, 457446, 461280, 465130, 467180, 468996, 484620, 487344, 487578, 495510, 496506, 497640, 499500, 500500, 501942, 503506, 507528.

Some larger examples :