a(n) = T(2n,n+2), T given by A027948.

Terms

a(0) =1a(1) =6a(2) =63a(3) =344a(4) =1383a(5) =4685a(6) =14323a(7) =41119a(8) =113590a(9) =306605a(10) =816410a(11) =2157046a(12) =5674578a(13) =14893364a(14) =39040633a(15) =102273950a(16) =267839033a(17) =701315739a(18) =1836198205a(19) =4807389285a(20) =12586103720a(21) =32951083211a(22) =86267338468a(23) =225851160284a(24) =591286410708