The first , 250, terms of the sequence "number of partitions of n into parts \
    with distinct multiplicities is

[1, 2, 2, 4, 5, 7, 10, 13, 15, 21, 28, 31, 45, 55, 62, 82, 105, 116, 153, 172,

    208, 251, 312, 341, 431, 492, 588, 676, 826, 905, 1120, 1249, 1475, 1676,

    2003, 2187, 2625, 2922, 3409, 3810, 4481, 4910, 5792, 6382, 7407, 8186,

    9527, 10434, 12104, 13308, 15293, 16825, 19332, 21193, 24281, 26590, 30264,

    33167, 37746, 41304, 46723, 51105, 57824, 63089, 71116, 77661, 87174, 95162,

    106767, 116276, 130086, 141975, 158109, 172158, 192196, 208750, 231985,

    252703, 279917, 304481, 337512, 365938, 404723, 440290, 484899, 526012,

    580656, 628704, 691427, 750854, 823135, 891834, 979467, 1058435, 1159767,

    1256880, 1371965, 1483751, 1623375, 1752443, 1911046, 2067456, 2249444,

    2429337, 2647532, 2852449, 3101167, 3350292, 3632299, 3916575, 4254015,

    4578913, 4961281, 5350317, 5786186, 6229771, 6744992, 7249767, 7834973,

    8438264, 9099153, 9782250, 10564186, 11342088, 12225064, 13143216, 14142579,

    15185699, 16355999, 17537617, 18859435, 20249551, 21740304, 23309862,

    25052839, 26830676, 28789722, 30864369, 33075342, 35421402, 37984022,

    40629214, 43513946, 46590045, 49835545, 53295668, 57045908, 60952531,

    65159723, 69668751, 74401163, 79476261, 84912875, 90619911, 96721671,

    103287973, 110130121, 117497296, 125334380, 133622042, 142393866, 151868166,

    161705680, 172335955, 183548697, 195467141, 208011607, 221601927, 235641300,

    250847732, 266797381, 283843814, 301654570, 320989996, 340913983, 362541686,

    385082756, 409262515, 434418643, 461778184, 489866305, 520392683, 552079521,

    586194919, 621502624, 659937596, 699321044, 742181954, 786463956, 834255416,

    883555471, 937267251, 992173017, 1051948501, 1113519332, 1180126172,

    1248576566, 1323165871, 1399318823, 1482270957, 1567435521, 1659678555,

    1754248355, 1857336621, 1962414004, 2076850407, 2194072607, 2321208607,

    2451231508, 2592891255, 2737192203, 2894320440, 3054910670, 3229181482,

    3407102533, 3600920587, 3798138044, 4012753123, 4231776835, 4469573493,

    4711985790, 4975800649, 5244141186, 5536011355, 5833446461, 6156363497,

    6485152020, 6842757583, 7206338990, 7601390509, 8003621810, 8440255173,

    8884410449, 9366957023, 9857479220, 10390079693, 10931848047, 11519618594,

    12117163210, 12765729427, 13425002589, 14139888851, 14866704845,

    15654865741, 16455709018, 17323894915, 18206361345, 19162301209,

    20133836524, 21186368654]

                        this took, 2449.476, seconds .