G.f.: A(x) = (1/2)*x*(B(x)^2+B(x^2)), where B(x) = g.f. for A000600.

Terms

a(0) =0a(1) =0a(2) =0a(3) =0a(4) =0a(5) =0a(6) =0a(7) =0a(8) =0a(9) =1a(10) =1a(11) =4a(12) =10a(13) =30a(14) =78a(15) =221a(16) =590a(17) =1619a(18) =4366a(19) =11858a(20) =32029a(21) =86744a(22) =234487a(23) =634630a(24) =1717133a(25) =4649560a(26) =12593571a(27) =34133104a(28) =92560816a(29) =251166524