a(n) = Sum_{k=1..n} binomial(n,k) * d(k), where d(k) = the number of positive divisors of k.

Terms

a(0) =1a(1) =4a(2) =11a(3) =27a(4) =62a(5) =137a(6) =296a(7) =630a(8) =1326a(9) =2768a(10) =5744a(11) =11867a(12) =24429a(13) =50135a(14) =102627a(15) =209641a(16) =427518a(17) =870579a(18) =1770536a(19) =3596614a(20) =7298397a(21) =14796658a(22) =29974913a(23) =60681233a(24) =122767148a(25) =248232863a(26) =501648844a(27) =1013257334a(28) =2045684971