a(n) = Sum_{k=n+1..2*n} T(n,k), T given by A027052.

Terms

a(0) =1a(1) =3a(2) =8a(3) =24a(4) =71a(5) =209a(6) =612a(7) =1784a(8) =5189a(9) =15081a(10) =43838a(11) =127528a(12) =371395a(13) =1082951a(14) =3161866a(15) =9243400a(16) =27055153a(17) =79280601a(18) =232567194a(19) =682905120a(20) =2007104343a(21) =5904004451a(22) =17380510458a(23) =51202600920a(24) =150942696637a(25) =445247984543