Related to partitions.

Terms

a(0) =1a(1) =2a(2) =4a(3) =8a(4) =21a(5) =52a(6) =131a(7) =316a(8) =765a(9) =1846a(10) =4494a(11) =10944a(12) =26654a(13) =64798a(14) =157502a(15) =382868a(16) =931028a(17) =2264106a(18) =5505777a(19) =13387880a(20) =32553601a(21) =79156974a(22) =192479838a(23) =468039888a(24) =1138098210a(25) =2767421826a(26) =6729311459a(27) =16363118556a(28) =39788886610a(29) =96751470494