G.f.: 1 / G(0), where G(k) = 1 - q^(k+1) / (1 - q^(k+1)/G(k+2) ).

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =8a(5) =17a(6) =36a(7) =76a(8) =162a(9) =345a(10) =734a(11) =1564a(12) =3332a(13) =7098a(14) =15124a(15) =32224a(16) =68658a(17) =146291a(18) =311704a(19) =664152a(20) =1415124a(21) =3015237a(22) =6424636a(23) =13689132a(24) =29167776a(25) =62148513a(26) =132421414a(27) =282153672a(28) =601192008a(29) =1280975135