a(n) = binomial(2*n,n) - ceiling(4^n/(2*sqrt(n))).

Terms

a(0) =0a(1) =0a(2) =1a(3) =6a(4) =23a(5) =87a(6) =335a(7) =1284a(8) =4929a(9) =18961a(10) =73116a(11) =282573a(12) =1094274a(13) =4245403a(14) =16498046a(15) =64209478a(16) =250241064a(17) =976467300a(18) =3814605426a(19) =14917391732a(20) =58391659033a(21) =228765630254a(22) =896981997531