"BIK" (reversible, indistinct, unlabeled) transform of 1,2,3,4...

Terms

a(0) =1a(1) =3a(2) =6a(3) =15a(4) =33a(5) =84a(6) =203a(7) =525a(8) =1330a(9) =3465a(10) =8955a(11) =23400a(12) =60957a(13) =159471a(14) =416702a(15) =1090635a(16) =2853229a(17) =7469052a(18) =19548759a(19) =51177225a(20) =133969386a(21) =350730933a(22) =918187991a(23) =2403833040a(24) =6293218393a(25) =16475822139a(26) =43134005238