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

Terms

a(0) =1a(1) =1a(2) =3a(3) =5a(4) =10a(5) =17a(6) =35a(7) =63a(8) =126a(9) =231a(10) =462a(11) =858a(12) =1716a(13) =3217a(14) =6435a(15) =12155a(16) =24310a(17) =46189a(18) =92378a(19) =176358a(20) =352716a(21) =676039a(22) =1352078a(23) =2600150a(24) =5200300a(25) =10029150a(26) =20058300a(27) =38779380a(28) =77558760a(29) =150270097