Number of multiset partitions of integer partitions of n with all distinct block sizes.

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =8a(5) =15a(6) =28a(7) =51a(8) =92a(9) =164a(10) =289a(11) =504a(12) =871a(13) =1493a(14) =2539a(15) =4290a(16) =7201a(17) =12017a(18) =19939a(19) =32911a(20) =54044a(21) =88330a(22) =143709a(23) =232817a(24) =375640a(25) =603755a(26) =966816a(27) =1542776a(28) =2453536a(29) =3889338