a(n) = T(2n,n+1), T given by A027948.

Terms

a(0) =1a(1) =4a(2) =25a(3) =97a(4) =309a(5) =894a(6) =2462a(7) =6610a(8) =17519a(9) =46135a(10) =121115a(11) =317484a(12) =831660a(13) =2177872a(14) =5702389a(15) =14929789a(16) =39087537a(17) =102333450a(18) =267913514a(19) =701407870a(20) =1836310955a(21) =4807525939a(22) =12586267895a(23) =32951278872a(24) =86267569944a(25) =225851432284a(26) =591286728337