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binomial coefficient  and  congruent n.

First numbers that belong to both sets:

6, 15, 20, 21, 28, 45, 55, 56, 70, 78, 84, 120, 126, 136, 165, 190, 210, 220, 231, 252, 253, 276, 286, 325, 330, 351, 406, 455, 462, 465, 495, 496, 561, 630, 703, 741, 792, 820, 861, 903, 924, 990, 1081, 1140, 1176, 1287, 1326, 1330, 1365, 1431, 1485, 1596, 1653, 1711, 1716, 1770, 1820, 1830, 2016, 2145, 2278, 2300, 2415, 2485, 2556, 2701, 2775, 2925, 2926, 3003, 3060, 3081, 3160, 3321, 3486, 3570, 3654, 3655, 3741, 3828, 4005, 4060, 4095, 4278, 4495, 4560, 4656, 4845, 4950, 4960, 5005, 5151, 5253, 5356, 5456, 5460, 5565, 5671, 5886, 5984, 6328, 6441, 6545, 6555, 6670, 6903, 7021, 7140, 7260, 7381, 7503, 7750, 8001, 8128, 8385, 8436, 8515, 8568, 8646, 8855, 8911, 9045, 9180, 9316, 9453, 9591, 9730, 9870, 9880, 10011, 10296, 10626, 10731, 10878, 11175, 11325, 11476, 11480, 11628, 11781, 11935, 12246, 12341, 12376, 12870, 12880, 13041, 13244, 13366, 13695, 13861, 14190, 14196, 14365, 14535, 14878, 14950, 15225, 15400, 15576, 15753, 16110, 16215, 16471, 16653, 17020, 17205, 17296, 17391, 17550, 17766, 17955, 18336, 18424, 18528, 18564, 19110, 19448, 19503, 19701, 19900, 20301, 20349, 20503, 20910, 21115, 21528, 21945, 22100, 22366, 22791, 23005, 23220, 23436, 23653, 23751, 23871, 24310, 24804, 24976, 25200, 25878, 26334, 26335, 26565, 27028, 27132, 27261, 27405, 27495, 27966, 28441, 28680, 28920, 29646, 30135, 30381, 30876, 31125, 31375, 31824, 31878, 32385, 32509, 32640, 32896, 33649, 33670, 34191, 34220, 34453, 34716, 35245, 35511, 35960, 35990, 36046, 36856, 37820, 37950, 38503, 38760, 38781, 39060, 39621, 39711, 39903, 40470, 40920, 41041, 41328, 41664, 41905, 42195, 42486, 42504, 43071, 43365, 43680, 43758, 43956, 44253, 44551, 44850, 45150, 46360, 46665, 47278, 47586, 47895, 47905, 48205, 48620, 48828, 49141, 49455, 50086, 50388, 51040, 52326.

Some larger examples :