a(n) = Sum_{k=1..2^n} d(k) where d(n) = number of divisors of n (A000005).

Terms

a(0) =1a(1) =3a(2) =8a(3) =20a(4) =50a(5) =119a(6) =280a(7) =645a(8) =1466a(9) =3280a(10) =7262a(11) =15937a(12) =34720a(13) =75108a(14) =161552a(15) =345785a(16) =736974a(17) =1564762a(18) =3311206a(19) =6985780a(20) =14698342a(21) =30850276a(22) =64607782a(23) =135030018a(24) =281689074a(25) =586636098a(26) =1219788256a(27) =2532608855a(28) =5251282902a(29) =10874696106