a(n) = Sum_{k=n..2*n} T(n,k), T given by A027052.

Terms

a(0) =1a(1) =1a(2) =4a(3) =10a(4) =27a(5) =77a(6) =220a(7) =632a(8) =1821a(9) =5257a(10) =15206a(11) =44068a(12) =127951a(13) =372173a(14) =1084382a(15) =3164498a(16) =9248241a(17) =27064057a(18) =79296978a(19) =232597316a(20) =682960523a(21) =2007206245a(22) =5904191878a(23) =17380855190a(24) =51203234981a(25) =150943862857a(26) =445250129556