G.f.: Sum_{k>=0} q(k)^3 * x^k / Sum_{k>=0} q(k)*x^k, where q(n) is A000009(n).

Terms

a(0) =1a(1) =0a(2) =0a(3) =6a(4) =0a(5) =18a(6) =30a(7) =60a(8) =66a(9) =258a(10) =402a(11) =606a(12) =1266a(13) =1866a(14) =3744a(15) =6864a(16) =9648a(17) =15432a(18) =30510a(19) =41166a(20) =72342a(21) =118140a(22) =178800a(23) =266262a(24) =441462a(25) =652164a(26) =1006410a(27) =1567692a(28) =2309958a(29) =3385554