Number of partitions of n that have hookset {1,2,...,k} for some k.

Terms

a(0) =1a(1) =1a(2) =2a(3) =2a(4) =3a(5) =4a(6) =4a(7) =6a(8) =7a(9) =9a(10) =10a(11) =16a(12) =14a(13) =23a(14) =24a(15) =33a(16) =33a(17) =50a(18) =50a(19) =71a(20) =75a(21) =101a(22) =103a(23) =146a(24) =151a(25) =201a(26) =211a(27) =280a(28) =292a(29) =389