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

Terms

a(0) =0a(1) =1a(2) =2a(3) =11a(4) =34a(5) =152a(6) =524a(7) =2207a(8) =7970a(9) =32744a(10) =121252a(11) =491988a(12) =1850380a(13) =7455944a(14) =28337976a(15) =113708295a(16) =435443490a(17) =1742630120a(18) =6711230900a(19) =26811568916a(20) =103711749284a(21) =413849297784