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binomial coefficient  and  pernicious n.

First numbers that belong to both sets:

6, 10, 20, 21, 28, 35, 36, 55, 56, 66, 70, 84, 91, 136, 171, 220, 253, 276, 286, 351, 364, 406, 465, 496, 528, 560, 595, 666, 820, 861, 1001, 1081, 1140, 1225, 1287, 1330, 1378, 1431, 1485, 1540, 1653, 1770, 1891, 2002, 2024, 2080, 2211, 2300, 2346, 2380, 2485, 2850, 3160, 3240, 3403, 3655, 3916, 4186, 4368, 4371, 4495, 4560, 4753, 4950, 4960, 5005, 5151, 5253, 5356, 5456, 5671, 5985, 6188, 6786, 7260, 7315, 7750, 8001, 8008, 8128, 8256, 8515, 8778, 8855, 9045, 9316, 9870, 10296, 10440, 10585, 10626, 11476, 11480, 12376, 12403, 12561, 12650, 12880, 13366, 13695, 13861, 14365, 16110, 16215, 16653, 16836, 17020, 17205, 17296, 17766, 18145, 18721, 19110, 19600, 20349, 20825, 21321, 21528, 21736, 22100, 22791, 23426, 23871, 24310, 24531, 24976, 25425, 25651, 25878, 26335, 26796, 27028, 27730, 29260, 29890, 30135, 31824, 32509, 32896, 33411, 33649, 33930, 34220, 34453, 34980, 35778, 35960, 35990, 38226, 38781, 41041, 41616, 41664, 42504, 43660, 46360, 46376, 48620, 48828, 49141, 49770, 50116, 50388, 51040, 51360, 53301, 53956, 54285, 56953, 60378, 61776, 62481, 62835, 63190, 64980, 65341, 67161, 67528, 68265, 68635, 70300, 70500, 71631, 72010, 72771, 73150, 73536, 73815, 74305, 75078, 76076, 77815, 80200, 81406, 82215, 82251, 85320, 85491, 86736, 87990, 88831, 91390, 92665, 95266, 96141, 97461, 97903, 98346, 98770, 99681, 101025, 102378, 104196, 109278, 111628, 112101, 113564, 114003, 114481, 114960, 117855, 118828, 119316, 119805, 120786, 122265, 123410, 124251, 124750, 126253, 128271, 131328, 132355, 133386, 134421, 134596, 135460, 135751, 137026, 139656, 141246, 142311, 143380, 143916, 144453, 144991, 147440, 148240, 148785, 151525, 152096, 152628, 154846, 161028, 161596, 162165, 162735, 163185, 163878, 164451, 165600, 166176, 167910, 167960, 168490, 170544, 171991, 173755, 174345, 176121, 177906, 178365, 184528, 186355, 187578, 188191, 189420, 190653, 191271, 193131.

Some larger examples :