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binomial coefficient  and  gapful n.

First numbers that belong to both sets:

105, 120, 165, 190, 220, 231, 253, 286, 300, 330, 462, 495, 561, 792, 990, 1001, 1035, 1140, 1275, 1330, 1365, 1485, 1540, 1770, 1771, 1820, 1830, 2002, 2080, 2300, 2380, 2600, 2775, 2925, 3003, 3060, 3240, 3276, 3570, 4005, 4095, 4186, 4368, 4560, 4960, 5005, 5050, 5151, 5995, 6188, 6435, 7140, 7770, 7875, 8008, 8256, 9180, 10153, 10440, 10660, 11175, 11325, 11440, 11480, 11628, 11781, 12090, 12650, 12720, 12870, 12880, 13244, 13530, 13695, 14190, 14535, 14950, 15180, 15225, 15400, 16110, 16215, 16290, 16653, 17020, 17205, 17296, 17391, 17550, 17955, 18336, 18424, 18564, 18915, 19110, 19600, 19701, 19900, 20100, 20475, 20825, 21736, 22100, 23220, 23426, 23751, 25200, 25425, 27720, 28680, 28920, 29260, 30135, 30628, 31465, 31824, 32640, 33930, 34980, 35245, 37950, 38760, 38781, 39060, 39711, 40920, 41041, 41328, 42504, 43680, 45760, 46360, 46665, 49455, 50403, 52650, 54285, 54615, 56616, 58905, 61425, 61776, 64620, 64980, 66066, 67161, 70125, 73150, 73920, 76076, 79079, 79800, 82160, 86320, 88560, 97020, 97461, 98280, 100576, 101025, 101270, 101475, 102340, 103740, 105570, 106030, 106491, 107880, 108345, 109278, 110685, 111930, 112101, 112575, 113050, 114960, 115440, 116280, 117370, 117480, 117855, 118755, 119805, 121485, 122265, 122760, 123410, 124750, 125250, 125580, 125970, 127260, 128271, 129795, 130305, 130816, 131328, 132870, 134940, 135460, 135751, 137550, 138075, 140715, 142845, 142880, 143380, 144991, 145530, 146070, 147440, 147696, 148240, 148785, 148995, 150975, 152096, 153735, 154290, 156520, 157080, 157641, 159330, 161028, 161700, 162165, 162735, 163185, 165600, 166176, 166650, 167910, 167960, 168490, 170820, 171405, 171700, 174345, 176121, 176715, 177100, 177310, 178365, 178503, 179700, 180300, 182710, 183315, 185136, 185745, 187460, 187578, 188805, 189420, 191890, 192510, 192920, 194580, 195000, 196251, 198135, 198765, 202566, 204480, 205120, 210925, 211575, 214840, 215820, 220116, 220780, 226128, 227475, 227920, 228826, 230181, 230300, 230860, 231540, 235641.

Some larger examples :