a(n) = binomial(2*n-5,n-2) + 2.

Terms

a(0) =2a(1) =2a(2) =3a(3) =3a(4) =5a(5) =12a(6) =37a(7) =128a(8) =464a(9) =1718a(10) =6437a(11) =24312a(12) =92380a(13) =352718a(14) =1352080a(15) =5200302a(16) =20058302a(17) =77558762a(18) =300540197a(19) =1166803112a(20) =4537567652a(21) =17672631902a(22) =68923264412a(23) =269128937222