a(n) = T(2n,n), T given by A026648.

Terms

a(0) =1a(1) =3a(2) =8a(3) =36a(4) =114a(5) =558a(6) =1856a(7) =9384a(8) =31942a(9) =164322a(10) =566928a(11) =2948184a(12) =10262004a(13) =53761068a(14) =188306112a(15) =991821456a(16) =3490234182a(17) =18458523378a(18) =65190481904a(19) =345875613144