a(n) = Sum_{k=0..n} p(k)^2, where p(k) is the partition function A000041.

Terms

a(0) =1a(1) =2a(2) =6a(3) =15a(4) =40a(5) =89a(6) =210a(7) =435a(8) =919a(9) =1819a(10) =3583a(11) =6719a(12) =12648a(13) =22849a(14) =41074a(15) =72050a(16) =125411a(17) =213620a(18) =361845a(19) =601945a(20) =995074a(21) =1622338a(22) =2626342a(23) =4201367a(24) =6681992a(25) =10515756a(26) =16449852a(27) =25509952a(28) =39333476a(29) =60172701