Repeated integer partitions or nested integer partitions.

Terms

a(0) =1a(1) =1a(2) =2a(3) =5a(4) =14a(5) =35a(6) =95a(7) =248a(8) =668a(9) =1781a(10) =4799a(11) =12890a(12) =34766a(13) =93647a(14) =252635a(15) =681272a(16) =1838135a(17) =4958738a(18) =13379885a(19) =36100214a(20) =97409045a(21) =262833314a(22) =709207394a(23) =1913652308a(24) =5163654671a(25) =13933178390a(26) =37596275726a(27) =101446960109a(28) =273737216768a(29) =738632652929