a(n) = binomial(n, floor(n/2)) + 1.

Terms

a(0) =2a(1) =2a(2) =3a(3) =4a(4) =7a(5) =11a(6) =21a(7) =36a(8) =71a(9) =127a(10) =253a(11) =463a(12) =925a(13) =1717a(14) =3433a(15) =6436a(16) =12871a(17) =24311a(18) =48621a(19) =92379a(20) =184757a(21) =352717a(22) =705433a(23) =1352079a(24) =2704157a(25) =5200301a(26) =10400601a(27) =20058301a(28) =40116601a(29) =77558761