a(n) = 1+Sum_{k=1..2^n-1} A000010(k).

Terms

a(0) =1a(1) =2a(2) =5a(3) =19a(4) =73a(5) =309a(6) =1229a(7) =4959a(8) =19821a(9) =79597a(10) =318453a(11) =1274563a(12) =5097973a(13) =20397515a(14) =81591147a(15) =326371001a(16) =1305482159a(17) =5222040189a(18) =20888133573a(19) =83552798667a(20) =334211074959