Riordan array (1/sqrt(1-2*x-3*x^2), M(x)-1) where M(x) is the g.f. of the Motzkin numbers A001006.

Terms

a(0) =1a(1) =1a(2) =1a(3) =3a(4) =3a(5) =1a(6) =7a(7) =9a(8) =5a(9) =1a(10) =19a(11) =26a(12) =19a(13) =7a(14) =1a(15) =51a(16) =75a(17) =65a(18) =33a(19) =9a(20) =1a(21) =141a(22) =216a(23) =211a(24) =132a(25) =51a(26) =11a(27) =1a(28) =393a(29) =623