a(n) = Sum_{k=0..n} q(k)^2, where q(k) = partition numbers into distinct parts (A000009).

Terms

a(0) =1a(1) =2a(2) =3a(3) =7a(4) =11a(5) =20a(6) =36a(7) =61a(8) =97a(9) =161a(10) =261a(11) =405a(12) =630a(13) =954a(14) =1438a(15) =2167a(16) =3191a(17) =4635a(18) =6751a(19) =9667a(20) =13763a(21) =19539a(22) =27460a(23) =38276a(24) =53160a(25) =73324a(26) =100549a(27) =137413a(28) =186697a(29) =252233