"AFK" (ordered, size, unlabeled) transform of 1,2,3,4,...

Terms

a(0) =1a(1) =1a(2) =2a(3) =7a(4) =10a(5) =25a(6) =68a(7) =111a(8) =208a(9) =435a(10) =1218a(11) =1773a(12) =3586a(13) =6077a(14) =12156a(15) =31961a(16) =47624a(17) =86825a(18) =151962a(19) =265525a(20) =469610a(21) =1242607a(22) =1750108a(23) =3217663a(24) =5263928a(25) =9205197a(26) =14713474a(27) =26440503a(28) =63610938a(29) =90877893