a(n) = Sum_{k=0..floor(n/2)} binomial(n,k) * binomial(2*k,n-2*k).

Terms

a(0) =1a(1) =0a(2) =2a(3) =6a(4) =10a(5) =40a(6) =110a(7) =294a(8) =938a(9) =2688a(10) =7932a(11) =24090a(12) =71434a(13) =215072a(14) =650078a(15) =1958866a(16) =5936970a(17) =18012384a(18) =54694100a(19) =166470324a(20) =507142300a(21) =1546756560a(22) =4723459622a(23) =14436872714a(24) =44166199466a(25) =135231887440a(26) =414370251700