a(n) = Sum_{k=0..n} p(k) where p(k) = number of partitions of k (A000041).

Terms

a(0) =1a(1) =2a(2) =4a(3) =7a(4) =12a(5) =19a(6) =30a(7) =45a(8) =67a(9) =97a(10) =139a(11) =195a(12) =272a(13) =373a(14) =508a(15) =684a(16) =915a(17) =1212a(18) =1597a(19) =2087a(20) =2714a(21) =3506a(22) =4508a(23) =5763a(24) =7338a(25) =9296a(26) =11732a(27) =14742a(28) =18460a(29) =23025