G.f.: Sum_{n>=0} x^n/(1 - x*(1+x)^(n+1)).

Terms

a(0) =1a(1) =2a(2) =4a(3) =8a(4) =17a(5) =38a(6) =90a(7) =225a(8) =593a(9) =1642a(10) =4762a(11) =14418a(12) =45443a(13) =148713a(14) =504149a(15) =1766929a(16) =6390719a(17) =23815167a(18) =91306967a(19) =359694456a(20) =1454213025a(21) =6027213530a(22) =25583995336a(23) =111118605582a(24) =493407322279