Number of Motzkin prefixes of length 2n and height n.

Terms

a(0) =1a(1) =3a(2) =13a(3) =64a(4) =334a(5) =1802a(6) =9933a(7) =55575a(8) =314362a(9) =1793126a(10) =10295625a(11) =59430043a(12) =344559826a(13) =2005026610a(14) =11703965955a(15) =68503652100a(16) =401892122682