a(n) = Sum_{k=0..n} T(n,k)*T(n,2n-k), T given by A027960.

Terms

a(0) =1a(1) =10a(2) =29a(3) =97a(4) =297a(5) =904a(6) =2685a(7) =7876a(8) =22823a(9) =65533a(10) =186691a(11) =528370a(12) =1486969a(13) =4164382a(14) =11613137a(15) =32264089a(16) =89339325a(17) =246645436a(18) =679111413a(19) =1865340568a(20) =5112351131a(21) =13983383605a(22) =38177371159a(23) =104055773542a(24) =283171508977