a(n) is the sum over all proper integer partitions with distinct parts of n of the previous terms.

Terms

a(0) =1a(1) =0a(2) =1a(3) =2a(4) =4a(5) =9a(6) =20a(7) =44a(8) =100a(9) =225a(10) =507a(11) =1145a(12) =2592a(13) =5858a(14) =13275a(15) =30043a(16) =68054a(17) =154132a(18) =349182a(19) =790954a(20) =1792001a(21) =4059646a(22) =9197535a(23) =20837459a(24) =47209682a(25) =106957699a(26) =242325918a(27) =549015961a(28) =1243864083a(29) =2818122854