Related to the set of Motzkin trees where all leaves are at the same unary height 2.

Terms

a(0) =0a(1) =1a(2) =0a(3) =1a(4) =1a(5) =3a(6) =2a(7) =9a(8) =7a(9) =27a(10) =25a(11) =85a(12) =86a(13) =287a(14) =296a(15) =975a(16) =1065a(17) =3369a(18) =3825a(19) =11887a(20) =13836a(21) =42389a(22) =50597a(23) =152549a(24) =186186a(25) =554103a(26) =688494a(27) =2027304a(28) =2559958a(29) =7461971