G.f.: Product_{j>=1} (1 + p(x^j)), where p(x) is the g.f. of A000040.

Terms

a(0) =1a(1) =2a(2) =5a(3) =11a(4) =22a(5) =43a(6) =78a(7) =140a(8) =238a(9) =405a(10) =665a(11) =1077a(12) =1710a(13) =2685a(14) =4140a(15) =6336a(16) =9551a(17) =14280a(18) =21117a(19) =30994a(20) =45051a(21) =65046a(22) =93170a(23) =132600a(24) =187439a(25) =263449a(26) =367999a(27) =511409a(28) =706833a(29) =972257