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

Terms

a(0) =1a(1) =6a(2) =20a(3) =58a(4) =161a(5) =436a(6) =1165a(7) =3088a(8) =8146a(9) =21426a(10) =56255a(11) =147538a(12) =386681a(13) =1013026a(14) =2653240a(15) =6948058a(16) =18193141a(17) =47634936a(18) =124717445a(19) =326526748a(20) =854877926a(21) =2238131506a(22) =5859556195a(23) =15340601158a(24) =40162350961a(25) =105146619486a(26) =275277778940