G.f.: x * Product_{k>=1} 1/(1 - a(k)*(-x)^k)^((-1)^k).

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =4a(5) =8a(6) =16a(7) =34a(8) =76a(9) =168a(10) =368a(11) =838a(12) =1964a(13) =4544a(14) =10464a(15) =24658a(16) =58984a(17) =140072a(18) =331456a(19) =795834a(20) =1932228a(21) =4665304a(22) =11227280a(23) =27305882a(24) =66953236a(25) =163418448a(26) =397826496a(27) =976658846a(28) =2412163316a(29) =5935476672