a(n) = Sum_{k=n+1..2*n} T(n, k), T given by A027023.

Terms

a(0) =1a(1) =4a(2) =11a(3) =34a(4) =103a(5) =306a(6) =901a(7) =2636a(8) =7685a(9) =22372a(10) =65111a(11) =189590a(12) =552547a(13) =1612154a(14) =4709369a(15) =13773368a(16) =40329465a(17) =118217992a(18) =346891115a(19) =1018872626a(20) =2995250535a(21) =8812601062a(22) =25948130525a(23) =76456539156a(24) =225427875325a(25) =665066293480