a(n) = Sum_{k=1..A003056(n)} 2^(T(n,k)-1), where T(n,k) = k-th term in row n of A235791.

Terms

a(0) =1a(1) =2a(2) =5a(3) =9a(4) =18a(5) =35a(6) =69a(7) =133a(8) =266a(9) =523a(10) =1043a(11) =2069a(12) =4133a(13) =8230a(14) =16459a(15) =32843a(16) =65675a(17) =131221a(18) =262421a(19) =524566a(20) =1049127a(21) =2097707a(22) =4195371a(23) =8389707a(24) =16779341a(25) =33556565a(26) =67113110a(27) =134221975a(28) =268443799a(29) =536879403