a(n) = Sum_{k=0..floor(n/2)} T(n,k), T given by A026747.

Terms

a(0) =1a(1) =1a(2) =4a(3) =5a(4) =18a(5) =25a(6) =84a(7) =124a(8) =398a(9) =612a(10) =1901a(11) =3012a(12) =9126a(13) =14800a(14) =43968a(15) =72658a(16) =212417a(17) =356544a(18) =1028520a(19) =1749344a(20) =4989477a(21) =8583258a(22) =24244139a(23) =42121079a(24) =117973702a(25) =206754379a(26) =574811040a(27) =1015179978a(28) =2803969443a(29) =4986329826