A024495 but with terms swapped in pairs.

Terms

a(0) =0a(1) =0a(2) =3a(3) =1a(4) =11a(5) =6a(6) =42a(7) =21a(8) =171a(9) =85a(10) =683a(11) =342a(12) =2730a(13) =1365a(14) =10923a(15) =5461a(16) =43691a(17) =21846a(18) =174762a(19) =87381a(20) =699051a(21) =349525a(22) =2796203a(23) =1398102a(24) =11184810a(25) =5592405a(26) =44739243a(27) =22369621a(28) =178956971a(29) =89478486