"BGK" (reversible, element, unlabeled) transform of 1,2,3,4,...

Terms

a(0) =1a(1) =1a(2) =2a(3) =5a(4) =8a(5) =18a(6) =40a(7) =77a(8) =180a(9) =378a(10) =822a(11) =1750a(12) =3824a(13) =8016a(14) =16630a(15) =36100a(16) =74092a(17) =154325a(18) =317388a(19) =657064a(20) =1348688a(21) =2732441a(22) =5554850a(23) =11203449a(24) =22725376a(25) =45309407a(26) =90568158a(27) =180428451a(28) =358348728a(29) =709098028