A bisection of the Motzkin numbers A001006.

Terms

a(0) =1a(1) =2a(2) =9a(3) =51a(4) =323a(5) =2188a(6) =15511a(7) =113634a(8) =853467a(9) =6536382a(10) =50852019a(11) =400763223a(12) =3192727797a(13) =25669818476a(14) =208023278209