"AFK" (ordered, size, unlabeled) transform of 2,2,2,2,...

Terms

a(0) =1a(1) =2a(2) =2a(3) =10a(4) =10a(5) =18a(6) =66a(7) =74a(8) =122a(9) =178a(10) =610a(11) =666a(12) =1146a(13) =1586a(14) =2450a(15) =6778a(16) =8026a(17) =12738a(18) =18258a(19) =27194a(20) =36938a(21) =96226a(22) =110578a(23) =177930a(24) =246474a(25) =368354a(26) =491426a(27) =717418a(28) =1543978a(29) =1874418