a(n) = Sum_{k = 1..n} floor(2^k / k).

Terms

a(0) =2a(1) =4a(2) =6a(3) =10a(4) =16a(5) =26a(6) =44a(7) =76a(8) =132a(9) =234a(10) =420a(11) =761a(12) =1391a(13) =2561a(14) =4745a(15) =8841a(16) =16551a(17) =31114a(18) =58708a(19) =111136a(20) =211000a(21) =401650a(22) =766372a(23) =1465422a(24) =2807599a(25) =5388709a(26) =10359735a(27) =19946715a(28) =38459505a(29) =74250899