Boustrophedon transform of 1 & primes: 1,2,3,5,7,...

Terms

a(0) =1a(1) =3a(2) =8a(3) =22a(4) =66a(5) =222a(6) =862a(7) =3838a(8) =19542a(9) =111894a(10) =712282a(11) =4987672a(12) =38102844a(13) =315339898a(14) =2810523166a(15) =26838510154a(16) =273374835624