a(n) = binomial(2*n,n) - ceiling(2^(2*n)/(n+1)).

Terms

a(0) =0a(1) =0a(2) =0a(3) =4a(4) =18a(5) =81a(6) =338a(7) =1384a(8) =5588a(9) =22405a(10) =89430a(11) =355906a(12) =1413600a(13) =5607109a(14) =22220902a(15) =88008656a(16) =348435254a(17) =1379169043a(18) =5458320734a(19) =21601368452a(20) =85488832259a(21) =338346669389