a(n) = Sum_{k=1..n} 2^k * sigma(k), where sigma(k) = A000203(k).

Terms

a(0) =2a(1) =14a(2) =46a(3) =158a(4) =350a(5) =1118a(6) =2142a(7) =5982a(8) =12638a(9) =31070a(10) =55646a(11) =170334a(12) =285022a(13) =678238a(14) =1464670a(15) =3496286a(16) =5855582a(17) =16079198a(18) =26564958a(19) =70605150a(20) =137714014a(21) =288708958a(22) =490035550a(23) =1496668510a(24) =2536855902a(25) =5355428190a(26) =10724137310a(27) =25756522846a(28) =41862650206a(29) =119172061534