a(n) equals the sum of path counts in the (right-aligned Ferrers plots of) the partitions of n.

Terms

a(0) =1a(1) =2a(2) =3a(3) =6a(4) =9a(5) =18a(6) =27a(7) =49a(8) =77a(9) =129a(10) =199a(11) =329a(12) =497a(13) =787a(14) =1194a(15) =1838a(16) =2738a(17) =4154a(18) =6108a(19) =9098a(20) =13265a(21) =19432a(22) =28024a(23) =40612a(24) =57961a(25) =82958a(26) =117469a(27) =166390a(28) =233520a(29) =327899