a(n) = Sum_{k=1..n-1} ((-1)^(k+n+1)*binomial(k,floor(k/2))).

Terms

a(0) =0a(1) =1a(2) =1a(3) =2a(4) =4a(5) =6a(6) =14a(7) =21a(8) =49a(9) =77a(10) =175a(11) =287a(12) =637a(13) =1079a(14) =2353a(15) =4082a(16) =8788a(17) =15522a(18) =33098a(19) =59280a(20) =125476a(21) =227240a(22) =478192a(23) =873886a(24) =1830270a(25) =3370030a(26) =7030570a(27) =13027730a(28) =27088870a(29) =50469890