a(n) = T(2*n, n-1), where T is given by A026584.

Terms

a(0) =1a(1) =2a(2) =9a(3) =38a(4) =140a(5) =701a(6) =2534a(7) =13294a(8) =48369a(9) =258430a(10) =947694a(11) =5114572a(12) =18872399a(13) =102539204a(14) =380143356a(15) =2075658454a(16) =7723000261a(17) =42330184638a(18) =157951859953a(19) =868376395790