a(0) = 1; for n > 0, a(n) = 1 + Sum_{k = 1..n} 2^k a(floor(log_2(k))).

Terms

a(0) =1a(1) =3a(2) =15a(3) =39a(4) =279a(5) =759a(6) =1719a(7) =3639a(8) =13623a(9) =33591a(10) =73527a(11) =153399a(12) =313143a(13) =632631a(14) =1271607a(15) =2549559a(16) =20834103a(17) =57403191a(18) =130541367a(19) =276817719a(20) =569370423a(21) =1154475831a(22) =2324686647a(23) =4665108279a(24) =9345951543a(25) =18707638071a(26) =37431011127a(27) =74877757239a(28) =149771249463