a(n) = T(2n-1,n-1) = T(2n,n+1), T given by A026725.

Terms

a(0) =1a(1) =4a(2) =16a(3) =65a(4) =267a(5) =1105a(6) =4597a(7) =19196a(8) =80380a(9) =337284a(10) =1417582a(11) =5965622a(12) =25130844a(13) =105954110a(14) =447015744a(15) =1886996681a(16) =7969339643a(17) =33670068133a(18) =142301618265a(19) =601586916703