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

Terms

a(0) =1a(1) =1a(2) =2a(3) =5a(4) =13a(5) =35a(6) =95a(7) =260a(8) =713a(9) =1959a(10) =5386a(11) =14815a(12) =40759a(13) =112151a(14) =308609a(15) =849240a(16) =2337009a(17) =6431246a(18) =17698332a(19) =48704714a(20) =134032593a(21) =368850417a(22) =1015056867a(23) =2793383746a(24) =7687248186a(25) =21154913043a(26) =58217239536a(27) =160210872557a(28) =440892153268